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# Integration by parts and roots

1. Feb 23, 2008

### jhayes25

Ok. I have a definite integral of e^sqroot(x) dx from x=0 to x=1.

I would use u=sqroot(x) and du=1/2*sqroot(x), but i'm confused what I would set v=?

2. Feb 23, 2008

### rocomath

$$\int_0^1 e^{\sqrt x}dx$$

3. Feb 23, 2008

### jhayes25

yes, haha thanks. I knew I would screw it up if i tried.

4. Feb 23, 2008

### rocomath

$$t=e^{\sqrt x} \rightarrow \ln t=\sqrt x$$ "evaluate for new limits" $$|_0^1=|_1^e$$

$$dt=\frac{e^{\sqrt x}}{2\sqrt x}dx \rightarrow 2\ln tdt=e^{\sqrt x}dx$$

$$2\int_1^e\ln tdt$$

Take it from here.

Last edited: Feb 23, 2008
5. Feb 23, 2008

### jambaugh

Remember that the "dx" is not just notation. In integrating by parts or in substitution you will need to account for it. However if you're trying to do this integral by parts you're not going to want to set $$u=\sqrt{x}$$ as this is not a factor of your integrand. For integration by parts you need the form:
$$\int u dv$$

I think you're first going to want to execute the variable substitution of $$u=\sqrt{x}$$ and see what integral you get. Then possibly it will be integrable by parts.

Remember that in executing substitution you either need to change your limits to those of the new variable (actually the same in this case) or you should rewrite your final integral back in terms of the original variable before you evaluate the limits.

6. Feb 23, 2008

### Count Iblis

As explained by jambaugh substitute x = t^2, then exp(sqrt(x)) = exp(t) and dx = 2t dt The limits x = 0 and x = 1 correspond to t = 1 and t = 1 respectively.

Try to do this integral using partial integration. Also try to do it by first computing the integral of exp(p t) where p is an arbitrary parameter and then differentiate both sides w.r.t. p.

7. Feb 23, 2008

### sutupidmath

$$\int_0^1 e^{\sqrt x}dx$$
another way of doing it would be like this
$$\int_0^1 e^{\sqrt x}dx=\int_0^1 \sqrt x \frac{e^{\sqrt x}}{\sqrt x }$$ And then take the sub
$$t=\sqrt x, so, dt=\frac{dx}{2 \sqrt x}=>2dt=\frac{dx}{\sqrt x}, x=0 => t=0, x=1=> t=1$$ then
$$\int_0^1 2t e^{t}$$ and now you could apply integration by parts, by letting u=t and $$v=\int e^{t}dt$$

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Re: programming problem about elements taken

• To: mathgroup at smc.vnet.net
• Subject: [mg72478] Re: [mg72470] programming problem about elements taken
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 31 Dec 2006 05:23:04 -0500 (EST)

For a sorted output:

choose1[a_?VectorQ, epsilon_?NumericQ]:=Module[
{sa=Sort[a]},
Fold[If[#2-Last[#1]>epsilon,
Append[#1,#2],#1]&,{First[sa]},Rest[sa]]];

To retain the original element order:

choose2[a_?VectorQ, epsilon_?NumericQ]:=Module[
{sa=Sort[a]},
Select[a,MemberQ[Fold[If[#2-Last[#1]>epsilon,
Append[#1,#2],#1]&,{First[sa]},Rest[sa]], #]&]];

a=Table[Random[],{20}]

{0.67319,0.378445,0.981498,0.579474,0.798173,0.537112,0.884835,0.534093,0.\
0471484,0.0516117,0.988746,0.570592,0.261828,0.632062,0.754747,0.436792,0.\
669037,0.149373,0.802271,0.484141}

choose1[a,0.1]

{0.0471484,0.149373,0.261828,0.378445,0.484141,0.632062,0.754747,0.884835,0.\
988746}

choose2[a,0.1]

{0.378445,0.884835,0.0471484,0.988746,0.261828,0.632062,0.754747,0.149373,0.\
484141}

%%==Sort[%]

True

However, the second method (original order) is much slower for a large list.

a=Table[Random[],{1000}];

Timing[choose1[a,0.1];]

{0.008364 Second,Null}

Timing[choose2[a,0.1];]

{1.23431 Second,Null}

Bob Hanlon

---- Barrow <GRseminar at gmail.com> wrote:
> Dear all,
>   I have a list of numbers (A),in fact, they are numbers distributed
> over [0,1].  Given parameter \epsilon, I have to choose elements from A
> such that their distances are larger than \epsilon, so the elements are
> "distringuishable". My goal is to find the maximum number of elements
> from A to meet the above "distinct criterion".
>   How to do it with the functions build-in in mathematica ??
>   Thanks in advence.           Sincerely           Barrow
>

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# Physical Reflection Models

Blinn-Phong is a cheap calculation of lighting but it is not an accurate model of how light physically distributes itself. We need to use electromagnetic theory to get even more realistic.

A bidirectional reflectance distribution function (BRDF) is a function which takes:

• as input: A direction $$\vec{L}$$ to a light source
• as input: A reflection direction $$\vec{R}$$
• as output: the amount of incident light from the direction $$\vec{L}$$ reflected in the $$\vec{R}$$ direction
##### Flux density

The power emitted by a light source or received by a surface per unit area, measured in watts per square meter, $$\frac{W}{m^2}$$.

Radiosity is the flux density emitted by a surface.

Irradiance of a light is the flux density incident on a surface.

The power emitted by the light source differs from teh power received by a surface due to the Lambertian effect, and it is modeled like so:

$\phi_I = \frac{P}{A} \ = \phi_E \left( \vec{N} \cdot \vec{L} \right)$

$\phi_E = \phi_I \frac{1}{\left( \vec{N} \cdot \vec{L} \right)} = \frac{P}{A \left( \vec{N} \cdot \vec{L} \right)}$

Where:

• $$\phi_E$$ is the light emitted by a light source
• $$\phi_I$$ is the light incident on a surface
• $$P$$ is the watts of power emitted by the light source.
• $$A$$ is area of the surface receiving the light
• $$\vec{N}$$ is the surface normal
• $$\vec{L}$$ is the unit vector pointing toward the light source.


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Hyperbolic tangent function. frequency f n = 5 Hz. There are still many un-explored areas for such places. At frequency. Tolbutamide is a weak acid with a pKa of 5. WALDEN UNIV 6560 FINAL EXAM (GRADED A) NURS 6560 FINAL EXAM (GRADED A The AGACNP is reviewing a chart of a head-injured patient. 147 Set ñ à Ô ë L ñ É Æ, as determined from Bode plot, and calculate 6 ñ à Ô ë L ñ É Æ3. Spatial frequency is typically measured in cycles or line pairs per millimeter (lp/mm), which is analogous to cycles per second (Hertz) in audio systems. Frequency response: Resonance, Bandwidth, Q factor Resonance. The input signal of the filter shown here has equal amplitude at frequencies ω 1 and ω 2. A typical question: What is the frequency and the phase angle of a sinusoidal waveform? Does "one" signal can really have a phase? Two "in-phase" waves have a phase (angle) of φ = 0 degrees. txt) or read online for free. Return the zero-frequency (or DC) gain of the given system: evalfr (sys, x) Evaluate the transfer function of an LTI system for a single complex number x. Then, we obtain. This is the procedure I used. As can be seen, the open-loop transfer function has been corrected with the crossover frequency ω c = 69. 2 s + 1 ! " # $% & Solution G p ( j !. The horizontal axis ranges from zero to π radians per sample. The FFT function in Matlab is an algorithm published in 1965 by J. Amplitude and Phase of the Frequency Response Function A useful tool in the dynamic analysis of structures is the frequency response function, or frf. This is used to recompress the files on a disk using the compression method specified. MTF is the spatial frequency response of an imaging system or a component; it is the contrast at a given spatial frequency relative to low frequencies. Frequency Response Preview. Use the frequency sampling method to design a 9-tap lowpass FIR filter with a cutoff frequency of 0. Using the figure above, we have ¾ C in: with C M2 open, the resistance seen by C in is equal. The function H (Ω) in equation (5. The FREQUENCY function calculates how often values occur within a range of values, and then returns a vertical array of numbers. Difference Equations and Impulse Responses. Filter two cosines. Amplitude, Period, Phase Shift and Frequency. How to Calculate Natural Frequencies and Mode Shapes of a PZT Disc in OnScale By Cyprien Rusu 18 July 2019 If you are familiar with OnScale, one of the things that you may be interested in learning is how to calculate natural frequencies of your model. repfreq returns the frequency response calculation of a linear system. FREQUENCY counts how often values occur in a set of data. , , converges Note that is also known as system frequency response Example 6. 000001 (a microsecond). The cutoff frequency denotes the frequency at which the two values are equal, ie $$R = X_C$$. m to calculate the average amplitude of the output response data for each of the prescribed periods. we directly model a transfer function using physical data. They are therefore, not surprisingly, related. so , at high frequencies , it will create some problems. Plot the magnitude (dB) of the response and comment on the slope outside of the cutoff frequency. The theory for such corrections assumes steady state motion and the correction is different depending on whether the calculation of the psd works with mass motion based on the acceleration response or the displacement response. So we are now prepared to calculate our circuits response at any frequency using algebra, instead of differential equations! ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = + + + + + + ⇒ L L 2 2 1 2 1 2 ( ) { ( )} ω ω ω ω ω ω j c j c H V e V e a b j b j L v t j t any j t any. Manually find the Frequency Response from the Transfer Function For a transfer function: = ( ) ( ) We have that: 𝜔= ( 𝜔) ∠ ( 𝜔) Where ( 𝜔)is the frequency response of the system, i. The response time is related to the bandwidth of the detector by BW = 0. The following article will attempt to explain the basic theory of the frequency response function. from x and y identify your transfer function (you must know the order of your system which is given by your frequency response). Trace F2, is the frequency response function shown as a plot of log amplitude (power spectrum) vs. Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. You need to find x(t)/y(t). Each time you move one column to the right of the original frequency cells, the column to be counted is shifted right from the first column you counted. Several methods are used for measuring sharpness that include the 10-90% rise distance technique, modulation transfer function (MTF), special and frequency domains, and slanted-edge algorithm. Finding the Frequency Response Analytically Given an LTI difference equation describing a filter, it is easy to analytically find an expression for the frequency response. It only takes a minute to sign up. Niknejad Lecture Outline Frequency response of the CE as voltage amp The Miller approximation. 25π are equal to 1 1 and the other samples are zero. A typical question: What is the frequency and the phase angle of a sinusoidal waveform? Does "one" signal can really have a phase? Two "in-phase" waves have a phase (angle) of φ = 0 degrees. Coronavirus crisis is the perfect time for millions of overweight Brits to get slim, Oxford University scientist says amid warnings obesity can DOUBLE the risk of being hospitalised with COVID-19. 92mm Connectors - May 07, 2020; Strategy Analytics - COVID-19 Will Reduce GaAs Revenue in 2020, but 5G Should Help it Recover - May 07, 2020. Hi all, I have input force data and output acceleration data to calculate frequency response functions. 2 Recommendations. Where: Δf = deviation BT = total bandwidth (for 98% power) fm = modulating frequency. It is commonly used to estimate the power transfer between input and output of a linear system. Notice that in all three cases, the frequency response has a lowpass characteristic. 0 is shown in the figure. The first part of the frf is the plot of amplitude versus frequency. In this tutorial we have seen how the range of frequencies over which an electronic circuit operates is determined by its frequency response. The total response consists of the sum of the complementary and the particular solution. How can the electricity system operator determine the optimal quantity and quality of electricity ancillary services (such as frequency response) to procure in a market increasingly characterized by. A root-mean-square (RMS) formulation translates the PSD curve for each response quantity into a single, most likely value. If G(s) is the open loop transfer function of a system and w is the frequency vector, we then plot G(j*w) versus w. Or we can measure the height from highest. A sinusoidal signal is the only signal in nature that is preserved by a linear system. The “length” of this interval of x values is called the period. You can use Excel's FREQUENCY function to create a frequency distribution - a summary table that shows the frequency (count) of each value in a range. 6 Using Forced Vibration Response to Measure Properties of a System. Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions. What are the period and frequency of y = ?; Using the formula we have period =. 2 Recommendations. •Common-mode disturbance at node P translates to a differential noise component at the output, if the supply voltage contains high-frequency noise and the circuit exhibits mismatches. For removing noise or cancellation of noise we use various type of digital. Frequency nadir map: 25% electronic generation (h2500quicks), mixed thermal-hydro fleet. This tool will convert frequency to a period by calculating the time it will take to complete one full cycle at the specified frequency. Find the steady-state response to a sum of sinusoidal inputs. Q, the test frequency, and the induc-tance. It plots the peak acceleration responses of a bank of single degree-of-freedom (SDOF) spring, mass damper systems all experiencing the same base-excitation as if on a rigid massless base. A root-mean-square (RMS) formulation translates the PSD curve for each response quantity into a single, most likely value. The output has a phase shift, φ, relative to. Using these settings PSPICE will calculate the sinusoidal steady state response of the circuit for the each of the frequencies indicated. This passive RC low pass filter calculator calculates the cutoff frequency point of the low pass filter, based on the values of the resistor, R, and the capacitor, C, of the circuit, according to the formula fc= 1/(2πRC). The short answer is because we are using a sine forcing function and that assumes that a long time has passed so that the exponential parts have had sufficient time to become zero, and the time domain coefficient of the remaining time function is the same as the coefficient of the frequency domain function so we get the same amplitude either way. Figure 6 depicts frequency response concept in a nutshell. The theory for such corrections assumes steady state motion and the correction is different depending on whether the calculation of the psd works with mass motion based on the acceleration response or the displacement response. To calculate the natural frequency using the equation above, first find out the spring constant for your specific system. Then, the Active High Pass Filter has a gain A F that increases from 0Hz to the low frequency cut-off point, ƒ C at 20dB/decade as the frequency increases. Typical Frequency response of an Amplifier F. , , converges Note that is also known as system frequency response Example 6. 8 krad/s and the phase margin being equal to 80°. To find frequency response, substitute s=jωin equation 22 2 1 R Hj L R LC L ω ω ωω = −+ 1 2 ()90 tan 1 R j L LC ω θω ω − =− − D Magnitude Response Phase Response-sL 1 2 1/sC Vi(s) R Vo(s) + ECE 307-5 4 Frequency Response of a Circuit At resonance frequency, the transfer function will be real. Tuckey for efficiently calculating the DFT. : Here, we will compute the phase and the magnitude of the voltage transfer function Vo/V1 for frequencies ranging from 10 Hz to 100 kHz. 9 Frequency Response of the Common-Emitter Amp Reading Assignment: 491-503 Amplifiers made with BJTs are similar to amplifiers made with op-amps—the both exhibit finite bandwidth. dstep (system[, x0, t, n]) Step response of discrete-time system. - The unit impulse function • Assume h(t) = 2e-2tu(t), calculate the Frequency Response:) 4 (3 4 3 3 3 20 2 J. Damping is typically fixed at a constant value, such as 5%, which is equivalent to an amplification factor of Q=10. The step input is used to measure the time response of the system. Sound is measured in terms of frequency. AME - Ampex Master Equalization Curve. the number of electrical magnetic poles. Use this utility to simulate the Transfer Function for filters at a given frequency, damping ratio ζ, Q or values of R and C. x(t) = cos. Step 3 - Calculate the slope. This response replaces the older "Linear" or "Unweighted" responses as these did not define the frequency range over which the meter would be linear. The program executes the following steps: 1. If the fundamental wave is set at 500 hertz, it experiences a first harmonic frequency at 1000 hertz, or double the fundamental frequency. Right-clicking on response plots gives access to a variety of options and annotations. Neatly draw the circuit and label each component's value. In this example, the amplitude response is. This table shows the frequency distribution for the data above. Amplitude Response. But it is far easier to calculate. The function HBP(jω) is called the standard second-order band-pass function. Calculate the frequency response function H(W) = Vout(W)/Vin(w) of the circuit below: 222 F V out 8-7. a usual mode for this oscillator is a feed back loop from emitter to collector via a capacitor. For the high frequency response using the poles of the transfer function only, we may approximate the cutoff in radians per second (ω) or Hertz (f) as π ω ω τ 2, 1 1 H H i i i eqi H i C R f ⎥ = = ⎦ ⎤ ⎢ ⎣ ⎡ ≅ ∑ ∑ −. As can be seen, the open-loop transfer function has been corrected with the crossover frequency ω c = 69. This method of calculating the frequency response of a digital filter is similar to the freqz function in Matlab ®. The “length” of this interval of x values is called the period. These vibrations cause the ski to lose contact with the ground. The input signal of the filter shown here has equal amplitude at frequencies ω 1 and ω 2. % Function to calculate steady state amplitude of % a forced linear system. Similar to the FFT Analyzer, the FRF is a characteristic of a system that has a measured response resulting from a known applied input. Example: Travel Survey. The amplitude is wrong and has a envelope outside. Simulateand iterate, if necessary. 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Plugging equation (9) into either (8a) or (8b) will lead to the frequency equation for a cantilever beam, (11) The frequency equation can be solved for the constants, k n L; the first six are shown below in Figure 3 (note, k n =0 is ignored since it implies that the bar is at rest because =0). If the input to a linear, time-invariant system is an eternal sinusoid, then the output is also an eternal sinusoid: • same frequency • possibly diﬀerent amplitude, and • possibly diﬀerent phase angle. Calculate h[n] Calculate h[n] analytically for the difference equation above. How to calculate the magnitude of Gain and Phase of a Transfer Function. One major complication in Frequency Response analysis is that in addition to the magnitude of the peak responses at each frequency calculation point, we also have a phase change. Divide the velocity by the wavelength. The paragraph just below the sliders shows how to calculate the value of the transfer function at that frequency, and it is a complex number with a magnitude (M) of 0. Browse other questions tagged filter frequency-response cutoff-frequency or ask your own question. It only takes a minute to sign up. Without digital filter we cannot think about proper communication because noise occurs in channel. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. , “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. HO: AMPLIFIER BANDWIDTH. Calculation between phase angle φ in radians (rad), the time shift or time delay Δ t, and the frequency f is: Phase angle (rad). If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input and output. we directly model a transfer function using physical data. frequency f n = 5 Hz. The following Matlab statements show how to use freqz to compute and plot the magnitude (absolute value) of the frequency response of a two-point averaging system as a function of ω in the range -π≤ω≤π:. However, as previously reported, low-frequency response obtained from the LSF method is not as good as that obtained from measurement of edge-spread function (ESF). Over the past years many have contested the conservatism of this assumption. Thomas Greve, Fei Teng, Michael Pollitt, Goran Strbac. NOTE: This answer is community wiki: If you feel there is a need for correction -please update the answer right here. Calculating the Spatial Frequency Response (SFR) The SFR is an absolute value of the Fourier transform of the LSF. This simple 555 Variable Frequency Square Wave Generator produces a variable frequency output of 2800Hz to 120KHz with this values. The concepts of frequency response, frequency range, audible frequencies, how frequency relates to musical notes, etc. In words, for a Linear Time-Invariant (LTI) system driven by a sinusoid input, the output is a sinusoid with same frequency, only its magnitude A and phase φ might change. Because spatial frequency is defined in terms of visual angle, a grating's spatial frequency changes with viewing distance. xi and xf are the initial and final values of x respectively. Divide the velocity of the wave, V, by the wavelength converted into meters, λ, in order to find the frequency, f. % K is nxn the stiffness matrix % M is the nxn mass matrix % f is the n dimensional force vector % omega is the forcing frequency, in radians/sec. WALDEN UNIV 6560 FINAL EXAM (GRADED A) NURS 6560 FINAL EXAM (GRADED A The AGACNP is reviewing a chart of a head-injured patient. The transient response relates the output to the input over time. Most people are relatively comfortable with time domain representations of signals. This table shows the frequency distribution for the data above. The response of a system can be partitioned into both the transient response and the steady state response. The proposed degradation index is based on the fictitious frequency response function method. Because FREQUENCY returns an array, it must be entered as an array formula. To show how the gain of an amplifier varies with frequency, a graph, showing the frequency response of the amplifier is used. We call the angle the phase. Frequency response permits analysis with respect to this. Amplitude Response. This plotting script employs the function cal_avg. "Unit step response" means that the forcing function (the step) has magnitude 1. Use this utility to simulate the Transfer Function for filters at a given frequency, damping ratio ζ, Q or values of R and C. This basic theory will then be used to calculate the frequency response function between two points on a structure using an accelerometer to measure the response and a force gauge hammer to measure the excitation. The frequency at this minimum voltage V min is the resonance frequency. In this tutorial we have seen how the range of frequencies over which an electronic circuit operates is determined by its frequency response. 3 As an alternative, this function can be represented in terms of its peak positive and peak negative responses. ) responds to a range of frequencies, we chart the results in the form of a frequency response graph. They are therefore, not surprisingly, related. AP* Waves & Sound Free Response Questions page 3 (b) Assume λ << d. 240 Mhz, 600kHz down from 146. Calculate the amplitude of the fundamental frequency component in vA and compare with the Fourier results in the simulation. Butterworth filter frequency response. A Bode plot is a standard format for plotting frequency response of LTI systems. The specified values for percent overshoot are: and for the settling time (in seconds), the specifications are. This document is an introduction to frequency response, and an introduction to active filters (filters using active amplifiers, like op amps). Coupler slope requirements in different octaves were found to be independent. Note that the second transfer function is just a delayed version of the first. SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 3. rose-hulman. FIR systems (i. Frequency Response Magnitude Frequency Response Phase. Does the frequency at which the transfer-function gain is peaking coincide with the L-C resonance frequency? Vs V soA()/ (). The function H (Ω) in equation (5. FREQUENCY RESPONSE OF LTI SYSTEMS � 12. freqz uses an FFT-based algorithm to calculate the Z-transform frequency response of a digital filter. A SYSTEM OPERATOR’S UTILITY FUNCTION FOR THE FREQUENCY RESPONSE MARKET. Frequency • What kind of filter is this?) 2 ( ) 0 {2 } tan (2. Thomas Greve, Fei Teng, Michael Pollitt, Goran Strbac. 01µF and C3=1nF, determine the frequency response and draw an. This page is a web application that design a Sallen-Key low-pass filter. Example: Your team has won 9 games from a total of 12 games played: the Frequency of winning is 9. The Excel RATE function is a financial function that returns the interest rate per period of an annuity. There is a related spreadsheet written by the author, op_amp_frequency_response. Per Unit Remnant Flux f 60 Frequency (leave units out so plotting works) Ï‰ 2 Ï€ f Angular frequency (leave units out so plotting works) L b X B Ï‰ Calculate burden inductance (keep unitless to simplify other calculations later) L b V RAT V RAT 1 Rem Include effects of remnant flux 1 X R I mag I rated N R B 1 Ï‰ L b 100 V RAT If. The hyperbolic tangent can be defined as: $$\operatorname{tanh}(x) = \frac{\operatorname{sinh}(x)}{\operatorname{cosh}(x)}$$ where sinh is the hyperbolic sine function and cosh. On physical examination, the heart rate is 100/min, blood. As the Butterworth filter is maximally flat, this means that it is designed so that at zero frequency, the first 2n-1 derivatives for the power function with respect to frequency are zero. The response can be given in terms of displacement, velocity, or acceleration. Z-weighting is a flat frequency response of 10Hz to 20kHz ±1. Amplitude, Period, Phase Shift and Frequency. Frequency Response of Transistor Amplifiers Simplest case: CE short-circuit current gain Ai(jω) as a function of frequency Kirchhoff's current law at the output node: Kirchhoff's current law at the input node: Solving for Vπ at the input node: Cπ Cµ rπ V gmVπ π + − Iin Io Io = gmVπ- VπjωCµ Is Vπ Zπ =where----- + VπjωCµ. Burkitt Lymphoma is mainly found as childhood tumor, yet it is, also, observed in adult patients (Huang. After passing through the high. Tolbutamide is a weak acid with a pKa of 5. Amplitude Response. Or system total impedance will be. Comparing the new frequency response waveform with original one, it can be easily found that the LC filter brings a dip to the original frequency response, the magnitude-frequency curve drops to close to 0 db in this case, and the phase-frequency curve also drops near that point, which makes the loop gain performance worse. If the frequency = 0 Hz, then there is no AC voltage - that's just DC. As this is hard to compare, these functions are reduced to a single number. Use this utility to simulate the Transfer Function for filters at a given center rejection frequency or values of R and C. The low frequency response was extended to more clearly reveal the "stepped" nature of the response. The response time is related to the bandwidth of the detector by BW = 0. of 20dB/decade, or 6dB/octave (an octave is a 2x change in frequency) • This relation to circuit natural frequencies also holds for higher order circuits • Allows us to quickly estimate (visualize) the frequency response based on the natural frequencies e6 e7 e8 e9 e10 e11-50-40-30-20-10 0 log (ω ). xls file (45 KB) How to use Key in the coefficients of the filter into the table, the frequency response will be generted automatically. Using these functions as building blocks, you can create additional measurement functions such as frequency response, impulse response, coherence, amplitude spectrum, and phase spectrum. Specifically, in the frequency domain, the gain vs. Finding the Frequency Response Analytically Given an LTI difference equation describing a filter, it is easy to analytically find an expression for the frequency response. Specifically, it reviews indications, details factors that influence results, presents a brief step-by-step protocol, outlines safety measures, describes proper patient preparation and procedures, and offers guidelines. Butterworth Filter Ideal Frequency Response. The various forms of frequency response function based on the type of response variable are also defined from a mechanical engineer-ing viewpoint. Power Spectral Densfty (PSD) is the frequency response of a random or periodic signal. Any input having a frequency below the cutoff frequency ωC gets attenuated or rejected. Cut-off frequency fc in Hz = 159155 / τ in µs. How to calculate FRF / Transfer function in python I've been perusing stack exchange and r/dsp but haven't found any useful questions on how to calculate a frequency response with a given input and output. The paragraph just below the sliders shows how to calculate the value of the transfer function at that frequency, and it is a complex number with a magnitude (M) of 0. A harmonic frequency is a regular and repeating multiple of an original wave pattern, known as a fundamental frequency. Frequency Response Experiment. Figure 25-1b shows the MTFs. You can model the diffraction as a loss function, a gain function, or you can model it inverted, which is useful if you want to subtract the baffle effect out of a frequency response curve. 20 to 20,000 Hz is generally accepted as the audible frequency range, this is the standard for most headphones. Frequency (50 Hz) Frequency (60 Hz) Slip - in synchronous electrical induction motors. 8-10 Hz can be influenced by resonant and. Calculate cutoff frequency of low pass filter. groups of size 3. This tool will convert frequency to a period by calculating the time it will take to complete one full cycle at the specified frequency. , it is multiplied by a unit step function). As the system is relatively simple, a discussion of how the ideas may be extended to more complex systems is included towards the end of the paper. The MEM scale values should match exactly in base-driven Frequency Response analysis and are an important check. At frequency. MTF is the spatial frequency response of an imaging system or a component; it is the contrast at a given spatial frequency relative to low frequencies. Using a single-frequency cosine as an input, for example, might lead to a disaster - if that frequency happens to exactly hit one of the frequencies tfestimate is using - since there would only be one input frequency on which to base an estimate for the response to all frequencies. Op-Amp Frequency Response 1 by Kenneth A. Butterworth Filter Ideal Frequency Response. TANH function Description. if you want design high frequency oscillator try CB amplifier , which is good for this aim. A spectrum represents the relative amounts of different frequency components in any signal. 5-63) Output is phase shifted from the input Frequency ωmust be in radians/time!!! (2πradians = 1 cycle) P = time/cycle = 1/(ν), 2πν= ω, so P = 2π/ω. In other words, it describes how accurately a system reproduces each frequency of an audio content, in terms of amplitude. The frequency response and step response are related, because they come from the same system. At the time constant of a second-order control system is 1/ζ ω n, the. Thus, at a frequency above the cutoff frequency, $$X_C$$ is less than $$R$$, at a. Both algorithms provide a spatial frequency response, so a function of response versus spatial frequencies. difference between the reactance of capacitor and inductor) hence in experiment the is always an change in value of current. 5V/μS, this. The two signals contain a 1-second and a 4-second cyclic pink. Raza et al. This app can be used to study the frequency response of an FIR filter with upto 30 coefficients. To plot the frequency response, we create a vector of frequencies (varying between zero or "DC" and infinity) and compute the value of the plant transfer function at those frequencies. signal, x(t) =Asinωt. Key words: shock response spectrum, shock, single degree of freedom szstem, measurements 1. From what I've read, it seems you want the amplitude and phase of this function in the frequency domain. A structure with the basic eigenvibration frequency of approx. Frequency response function (FRF) is the characteristic of a structure that has a measured or computed response resulting from a unit harmonic input. Boyd EE102 Lecture 10 Sinusoidal steady-state and frequency response †sinusoidalsteady-state †frequencyresponse †Bodeplots 10{1. In your example, poles at s=-2 and -3 do not mean that the TF has infinite gain at any particular frequency. repfreq returns the frequency response calculation of a linear system. 355 Hz, a transfer function correction would have been necessary. (The response can be measured as displacement, velocity or acceleration. frequency response function and is typically a function of frequency,. Help 1-10 ms to Hz. Cut-off frequency fc in Hz = 159155 / τ in µs. Transfer Functions and Bode Plots Transfer Functions For sinusoidal time variations, the input voltage to a ﬁlter can be written vI(t)=Re Vie jωt ¤ where Viis the phasor input voltage, i. Open image in new window Fig. Solved: how to make a MEASURE in which pass multiple filters in calculate function. If the input to a linear, time-invariant system is an eternal sinusoid, then the output is also an eternal sinusoid: • same frequency • possibly diﬀerent amplitude, and • possibly diﬀerent phase angle. see the conversion process from a continuous-frequency function to a repeating discrete-frequency function. Both sfrmat3 and Mitre SFR 1. (Usually the transfer function measures in Laplace domain and frequency response in frequency domain). Or system total impedance will be. Trace F2, is the frequency response function shown as a plot of log amplitude (power spectrum) vs. That's all the frequency response of a system/filter tells you, i. Impulse Responses We just saw how we can derive the response to an arbitrary periodic function by decomposing the function into a sum of sinusoids and cosines. An important property of discrete-time linear time-invariant systems is that it preserves the frequency of sinusoidal signals, only the phase shift and the amplitude are altered. where x is the input sequence, X is the DFT, and n is the number of samples in both the discrete-time and the discrete-frequency domains. signal, x(t) =Asinωt. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. Help 1-10 ms to Hz. A few years ago, I’ve created a reliable and low-cost SNMP device to monitor and control a data center environment, and on this post, I’ll walk you through the entire design process I went. Here, the frequency response near the crossover frequency is not changed Minimizes the added phase lag at the crossover frequency 5. Niknejad Prof. SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 3. Frequency response functions are complex functions, with real and imaginary components. Things to try. 2 Transfer function standard form Consider a rational transfer function H(s) in which all the poles and zeros are shown in a. because below MEASURE is not working with multiple filter only. An example of measuring the magnitude of the frequency response is given in Section 1. #N#At the cut-off frequency fc of a drop, the voltage V is always fallen to the value of 1/√2 and the voltage level is damped to 20 × log (1/√2) = (−)3,0103 dB. This page is a web application that design a Twin-T notch filter. Frequency Response Experiment. The proposed degradation index is based on the fictitious frequency response function method. Frequency Response Balancing Authority Name: My BA Balancing Authority Frequency Response Obligation (FRO from FRS Form 1) ‐80 Note: See "Instruction" tab for more detailed instructions. sometimes referred to a “transfer function” between the input and output. The plot (shown in Figure 6) still shows the response versus the frequency in Hertz though. Recall that if an LTI system H:[DiscreteTime → Reals] → [DiscreteTime → Reals] has impulse response h: DiscreteTime → Reals, and if the input is x: DiscreteTime → Reals, then the output is given by the convolution sum. Using PSPICE simulate the 2nd order High Pass Bessel Filter in Figure 5 using (3) to find the values of the components. Frequency response data is sometimes supplied with an instrument and can be found empirically. Typical Frequency response of an Amplifier F. Presumably a. Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions. Frequency Response and Impulse Response. frequency in Hertz) can also easily be calculated. Calculate and plot the response of an undamped system to a step function with a finite rise time of t1 for the case m=1 kg, k=1 N/m, t1=4s, and F0=20 N. Because FREQUENCY returns an array, it must be entered as an array formula. Voltage squared over load resistance, would be power. Sign up to join this community. It is separated into real and imaginary parts which are plotted on the real and imaginary axes to get the locus on the complex plane as ω is varied. Calculate Úfrom ö à Ô ë Ú L 1sin ö à Ô ë 1sin ö à Ô ë L0. Display this answer in Hertz as well. 1a shows the typical frequency response curve of an audio amplifier, and Fig. How to calculate the magnitude of Gain and Phase of a Transfer Function. At the time constant of a second-order control system is 1/ζ ω n, the. from x and y identify your transfer function (you must know the order of your system which is given by your frequency response). Other response quantities such as the velocity and acceleration of the mass can also be used to define a transfer function for various applications. f is frequency; f 50 is the frequency where MTF = 0. where - Angular frequency - Constant scaling frequency - Order of the filter - Parameter that characterizes ripple - Chebyshev function of degree. the angular frequency ω = 2π), and the zero phase θ = 0. Normally, frequency refers to the rate of repetitions per unit time, that is, the number of cycles per second (Hertz). Time constant and cut-off frequency. You do this by dividing the voltage by 0. In such graphs, it is common that very large values may be encountered for both gain and frequency. The cross-over frequency is the frequency at which the magnitude has a gain of 1 (or 0dB). HO: AMPLIFIER BANDWIDTH. To use this calculator, all a user must do is enter any 2 values in the field, and the calculator will compute the value of third field. functions of sines and cosines. This is a graphical tool to represent and calculate frequency response. The response is calculated at multiple points between the lowest frequency of interest and the first eigenfrequency in the range, between each eigenfrequency in the range, and between the last eigenfrequency in the range and the highest frequency in the range as illustrated in Figure 1. Q, the test frequency, and the induc-tance. Using all this, you can use the package to explore the associations of (the lifting of) governmental measures, citizen behavior and the Covid-19 spread. 000000322 = 993788819. The SciPy generated frequency response is correct. Frequency response data is sometimes supplied with an instrument and can be found empirically. where x is the input sequence, X is the DFT, and n is the number of samples in both the discrete-time and the discrete-frequency domains. The frequency response of H(z) is obtained by evaluating H(z) at points on the unit circle, with frequency going from 0 to w s /2 or equivalently with the phase angle of z going from 0 to pi radians. Note that the frequency response of a practical filter cannot be absolutely flat in the passband or in the stopband. In this lab, we will use the Frequency Response program in VEE to determine the frequency response of two filter circuits. The frequency response of the system is usually represented in terms of the complex frequency variable. This needs significant research efforts and good communication systems. Similar to the FFT Analyzer, the FRF is a characteristic of a system that has a measured response resulting from a known applied input. If G(s) is the open loop transfer function of a system and w is the frequency vector, we then plot G(j*w) versus w. The frequency response H (Ω) of T can be approximated by H (Ω) = ˆ 1 2 e −jΩ, 0 ≤ |Ω| ≤ Ω c 0, Ω c < |Ω| ≤ π. of EECS, The University of Michigan, Ann Arbor, MI 48109-2122 I. This attempt to reclaim the word ‘chemical’ from the advertising and marketing industries that use it as a synonym for poison was a reaction to a decision of the Advertising Standards. the total impedence is equal to square root of sum of squares of resistance in resistor and total reactance in the circuit(i. Get the interest rate per period of an annuity. But there is a simpler way. Butterworth filter frequency response. k is the slope of the line. Without digital filter we cannot think about proper communication because noise occurs in channel. From what I've read, it seems you want the amplitude and phase of this function in the frequency domain. A common feature of cloud-based infrastructures like Azure Storage is that they provide a highly available and durable platform for hosting data and applications. The formula used to calculate the frequency is: f = 1 / T. wmax = 20 ; % Maximum radian frequency magnitude for graph dw = 0. Using spectral analysis techniques, the frequency response function is calculated using the excitation and response signals. data_array Required. To calculate the magnitude, both real and imaginary portions of the function need to be used: dB 2 2 0 1 H(j ) 20log 1 ω= ω + ω (6) Equation 6 shows that at a frequency much lower than ω 0, the magnitude is near 1 V/V or 0 dB. 1) We refer to Ω 0 as the angular frequency of the sinusoid, measured in radians/sample; Ω 0 is the number of radians by which the argument of the cosine increases when n increases by 1. Thus it is possible to derive the formula for the Butterworth filter frequency response: |. This passive RC high pass filter calculator calculates the cutoff frequency point of the high pass filter, based on the values of the resistor, R, and the capacitor, C, of the circuit, according to the formula fc= 1/(2πRC). The plot (shown in Figure 6) still shows the response versus the frequency in Hertz though. Wireless sensor network in aqueous medium has the ability to explore the underwater environment in details. Frequency and period are used to measure properties of waves (e. If the damping b gets too large then, for the. The response can be given in terms of displacement, velocity, or acceleration. 1 Different forms. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response. Frequency Response Function Model Consider a linear system as represented by the diagram in Figure 1. frequency response function and is typically a function of frequency,. To convert degrees to radians you use the RADIANS function. The printout for box five produced a straight line. The frequency response of H(z) is obtained by evaluating H(z) at points on the unit circle, with frequency going from 0 to w s /2 or equivalently with the phase angle of z going from 0 to pi radians. A root-mean-square (RMS) formulation translates the PSD curve for each response quantity into a single, most likely value. This passive RC low pass filter calculator calculates the cutoff frequency point of the low pass filter, based on the values of the resistor, R, and the capacitor, C, of the circuit, according to the formula fc= 1/(2πRC). Neatly draw the circuit and label each component's value. The Frequency Response Functions. Use freqresp to compute the frequency response over a set of frequencies. A typical question: What is the frequency and the phase angle of a sinusoidal waveform? Does "one" signal can really have a phase? Two "in-phase" waves have a phase (angle) of φ = 0 degrees. In this lab, we will use the Frequency Response program in VEE to determine the frequency response of two filter circuits. As the system is relatively simple, a discussion of how the ideas may be extended to more complex systems is included towards the end of the paper. The horizontal axis ranges from zero to π radians per sample. The transfer functions of both the PI controller and the open-loop gain are depicted in Fig. PHARM 1. This graph shown below uses the WINDOW X: (-2, 4, 1) and Y: (-2, 2, 1). Wireless sensor network in aqueous medium has the ability to explore the underwater environment in details. The plots in Figure 7 are thus often called the transfer. This needs significant research efforts and good communication systems. Response Characteristics. For this you can assume a harmonic forcing function, for example: Y(t) = Y0 sin(wt) and corresponding displacement function: X(t) = X0 sin(wt-phi), where phi is the phase lag between applied force and resultant displacement. = input output Magnitude 20log10 (1). frequency f n = 5 Hz. Then, when you display the 8 cycle/degree grating, the center of the response profile shifts to lower frequencies (bottom-right graph above). An estimate of the amplifier bandwidth is provided by the frequency f H at which the gain drops 3dB below its value at mid-band (A M). If you need to calculate the frequency from the time it takes to complete a wave cycle, or T, the frequency will be the inverse of the time, or 1 divided by T. Both sfrmat3 and Mitre SFR 1. Zoom trace, Z2, is used to expand the vertical scale of the frequency response plot to 1 dB per division. 5 and a phase angle (θ) of -63. Set up an AC analysis of the circuit shown in Figure 6. [email protected] What is important here is the time variation of the air pressure from some ambient value rather than the. Frequency response function (FRF) is the characteristic of a structure that has a measured or computed response resulting from a unit harmonic input. Do not disassemble the active filters, they will be used in the Lab 4. We can find the transient response by using Fourier integrals. Frequency Response and Impulse Response. Figure 9-6 illustrates these relationships. The general representation of the frequency response of the system is shown in the figure below: As shown in the figure above the frequency response of the system can be thought of as the transfer function of the system in the frequency domain. The frequency response H(jw) is a function that relates the output response to a sinusoidal input at frequency w. freqz determines the transfer function from the (real or complex) numerator and denominator polynomials you specify and returns the complex frequency response, H ( e jω ), of a digital filter. To use this calculator, all a user must do is enter any values into any of the 2 fields, and the calculator will calculate the third field. Most people are relatively comfortable with time domain representations of signals. System Function H(f ) • The system function H(f) is a complex-valued function of frequency f. This -3dB cutoff frequency calculator calculates the -3dB cutoff point of the frequency response of a circuit, according to the formula, fC=1/(2πRC). How you can calculate if the op amp can handle a certain voltage at a certain frequency is determined by the formula, slew rate= 2πfV. If the frequency = 0 Hz, then there is no AC voltage - that's just DC. System Function H(f ) • The system function H(f) is a complex-valued function of frequency f. the frequency response is calculated between 100 rad/s and 10 krad/s. Note that each 2-pole section provides a maximum 180° of phase shift; and at the extremities, a phase shift of –180°, though lagging by 360°, is an angle with the same properties as a phase shift of 180°. We often measure the natural frequency and damping coefficient for a mode of vibration in a structure or component, by measuring the forced vibration response of the system. \$\begingroup\$s is sometimes referred to as frequency because of the close relationship between the Laplace transform and the Fourier transform. (The response can be measured as displacement, velocity or acceleration. The theory for such corrections assumes steady state motion and the correction is different depending on whether the calculation of the psd works with mass motion based on the acceleration response or the displacement response. Becoming familiar with this format is useful because: 1. Frequency response functions are complex functions, with real and imaginary components. However, computationally efficient algorithms can require as little as n log2(n) operations. Typical Frequency response of an Amplifier F. Within New Jersey there were at least three different chromate chemical manufacturing companies operating, one in Kearny, New Jersey, and the other two in. You need to find x(t)/y(t). Specifically, it reviews indications, details factors that influence results, presents a brief step-by-step protocol, outlines safety measures, describes proper patient preparation and procedures, and offers guidelines. Calculate and plot the response of an undamped system to a step function with a finite rise time of t1 for the case m=1 kg, k=1 N/m, t1=4s, and F0=20 N. Frequency Response Experiment. Frequency response. The frequency response is a plot of the magnitude M and angle φ as a function of frequency ω. The most common transfer function measurement is the FRF, or frequency response function. Finding the Frequency Response Analytically Given an LTI difference equation describing a filter, it is easy to analytically find an expression for the frequency response. The shock response spectrum is the peak absolute acceleration response of each SDOF system to the time history base input. If this is the correct assumption to make, then you will need to make a lot more specifications. Calculating the Spatial Frequency Response (SFR) The SFR is an absolute value of the Fourier transform of the LSF. 5-63) Output is phase shifted from the input Frequency ωmust be in radians/time!!! (2πradians = 1 cycle) P = time/cycle = 1/(ν), 2πν= ω, so P = 2π/ω. Figure 1: Bode plot of FRF Amplitude (Top) and Phase (Bottom). If you need to calculate the frequency from the time it takes to complete a wave cycle, or T, the frequency will be the inverse of the time, or 1 divided by T. Presumably a. This would be similar to estimating the acoustics of a concert. Calculate the frequency-response of the transfer function model, sys, at 100 frequency points. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. We most often look at this function in its modulus and phase form, and typically, the form of the complex function is a polynomial in j. 2K :, R3 51K :, C1 4. The specifications for the system's step response that are often used are the percent overshoot and the settling time. An example of each of these is shown in Figure 19-7. Recall that if the input x is a complex exponential, then the output y will be the same complex exponential scaled by the frequency response evaluated at the frequency of the. Calculate the frequency response function H(W) = Vout(W)/Vin(w) of the circuit below: 222 F V out 8-7. Lab Elec 08 - Frequency Response of the RC Network - Free download as PDF File (. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. The thick green line is the calculated frequency response of the corresponding generalized loudspeaker. A constant component (zero frequency) in the input passes through the filter unattenuated. This is because the reactance of the capacitor is high at low frequencies and blocks any current flow through the capacitor. frequency vector – in rad/sec mag: system gain response vector phase: system phase response vector – in degrees If no outputs are specified, bode response is automatically plotted – preferable to plot yourself Frequency vector input is optional. The fundamental frequency is the lowest frequency in a resonating system. Let's continue the exploration of the frequency response of RLC circuits by investigating the series RLC circuit shown on Figure 1. from your frequency response, calculate a temporel pulse response h(t) (it's the inverse Fourier transform of your frequency response; choose a white band signal x(t), and calculate y(t)=x(t)*h(t) (* is convolution). - When the transfer function for a component is. This statement provides practical guidelines for the 6-minute walk test (6MWT). Create your “Bin Array. Frequency response function (FRF) is the characteristic of a structure that has a measured or computed response resulting from a unit harmonic input. How to Calculate Natural Frequencies and Mode Shapes of a PZT Disc in OnScale By Cyprien Rusu 18 July 2019 If you are familiar with OnScale, one of the things that you may be interested in learning is how to calculate natural frequencies of your model. In this example, the amplitude response is. = input output Magnitude 20log10 (1). A harmonic frequency is a regular and repeating multiple of an original wave pattern, known as a fundamental frequency. 7) Using the schematic above for the ac, plot the transfer function V s V s oA ( )/ ( ). Finding the Frequency Response Analytically Given an LTI difference equation describing a filter, it is easy to analytically find an expression for the frequency response. To take the example of a typical broadcast FM signal that has a deviation of ±75kHz and a maximum modulation frequency of 15 kHz, the bandwidth of 98% of the power approximates to 2 (75 + 15) = 180kHz. The low damping ratio will give us a resonant peak in the frequency response (as well as much overshoot in the step response if we were interested in that). edu/~doering/ece. As the impulse response of the filter decays to zero, it is not necessary to use a windowing function. Hyperbolic tangent function. Use freqresp to compute the frequency response over a set of frequencies. Within New Jersey there were at least three different chromate chemical manufacturing companies operating, one in Kearny, New Jersey, and the other two in. Lp/mm is most appropriate for film. The problem is that the information 'between' the bins is lost and cannot be easily interpolated. Example: If the repeater output is 146. That's all for today! If you like this article, there are 2 things you can do for me: 1- Help me to share this article on Linkedin, facebook, twitter or in your habitual forum to help more people understand frequency response analysis (use the share button on the left of the article). A few years ago, I’ve created a reliable and low-cost SNMP device to monitor and control a data center environment, and on this post, I’ll walk you through the entire design process I went. To perform "black-box" characterization of a system using frequency response methods. Some headphones offer wider ranges. 1b, that of a RF amplifier. ” In this example, enter – in ascending order – the ages that you want to find the “frequency of occurrences” between; Select the “Array of Cells” that will contain your FREQUENCY() Function results. where - Angular frequency - Constant scaling frequency - Order of the filter - Parameter that characterizes ripple - Chebyshev function of degree. To calculate the magnitude, both real and imaginary portions of the function need to be used: dB 2 2 0 1 H(j ) 20log 1 ω= ω + ω (6) Equation 6 shows that at a frequency much lower than ω 0, the magnitude is near 1 V/V or 0 dB. 25π radians/sample. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. 0 * 10-4 for f 1 ≥ 8 Hz. The second harmonic frequency occurs at 1500 hertz, which is triple the fundamental. • For a given system, H(f) is obtained by measuring the system output VO in response to a sinusoidal input VS and then taking the ratio H(f)=VO/VS where VO and VS are phasors. Consider a process whose input, e. The frequency response of the system is usually represented in terms of the complex frequency variable. When the signal frequency is in the range of bandwidth, the filter will allow the signal with input impedance. Calculate natural frequency and damping coefficient; observe changes as a result of temperature and material; b. If the frequency = 0 Hz, then there is no AC voltage - that's just DC. The formula used to calculate the frequency is: f = 1 / T. The high-pass filter has a gain response with a frequency range from ω C to infinity. LINEAR TIME-INVARIANT SYSTEMS AND THEIR FREQUENCY RESPONSE Professor Andrew E. A common feature of cloud-based infrastructures like Azure Storage is that they provide a highly available and durable platform for hosting data and applications. Similar to the FFT Analyzer, the FRF is a characteristic of a system that has a measured response resulting from a known applied input. frequency response[′frē·kwən·sē ri‚späns] (engineering) A measure of the effectiveness with which a circuit, device, or system transmits the different frequencies. The plots in Figure 7 are thus often called the transfer. In simplest terms, if a sine wave is injected into a system at. That is, there is one item that is 60 or less; three items from 81 through 85, and so on. frequency respond. The time response of the system is thus a function of the natural frequency of the system, the damping ratio, and the forcing function, F(t). If the data are complex in the frequency domain, e. By using this website, you agree to our Cookie Policy. x(t) = cos. However, I don't know why the signal obtained from a sine wave input is so strange. As an example Let's think, Force matrix =a Acceleration. The frequency response is a plot of the magnitude M and angle φ as a function of frequency ω. If sys(s) is the transfer function of Sys, repf(k) equals sys(s) evaluated at. In this paper is simulated the time- domain unit sample response of sine function and frequency- domain response of sine function. Georgia Tech ECE 3040 - Dr. Useful variants such as phase delay and group delay are defined, and examples and applications are considered. 1 Different forms. Anything above ω C passes through unaffected. Becoming familiar with this format is useful because: 1. 37 Figure 27. , “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys.$\begingroup\$ While the editing has improved the answer a little, there are still many problems that are unresolved. 37 Figure 26. Similar to the FFT Analyzer, the FRF is a characteristic of a system that has a measured response resulting from a known applied input. To calculate the number of hours between two times, you can use a formula that simply subtracts the start time from the end time. 20 to 20,000 Hz is generally accepted as the audible frequency range, this is the standard for most headphones. Sharpness is most visible on features like image edges (Figure 2) and can be measured by the edge (step) response. They are somewhat intuitive and do not necessarily corre-spond to electrical analogies. Note that the second transfer function is just a delayed version of the first. Or we can measure the height from highest. Frequency Response Magnitude Frequency Response Phase. In its simplest form, freqz accepts the filter coefficient vectors b and a, and an integer p specifying the number of points at which to calculate the frequency response. Burkitt Lymphoma Essay Burkitt Lymphoma was mapped out in geographic distribution across Africa by Dr. You can find natural frequency and damping ratio by comparing above t transfer function with a general 2nd order transfer function. There are still many un-explored areas for such places. The fundamental frequency is the lowest frequency in a resonating system. We express the filter as a transfer function with the help of the z-transform and the complex exponential. Calculate the Q factor using the equation from. , the system's response to an input signal can be found as the linear combination of its responses to the components of the signal, or. Superposition and the Frequency Response ECE 2610 Signals and Systems 6-6 Superposition and the Frequency Response † We can use the linearity of the FIR filter to compute the out-put to a sum of sinusoids input signal † As a special case we first consider a single real sinusoid (6. This page is a web application that design a RC low-pass filter. Squaring the quantity prior to it entering the logarithm, means that you calculate it as 20*log base 10 of your voltage gain magnitude. Calculation between phase angle φ° in degrees (deg), the time delay Δ t and the frequency f is: Phase angle (deg) (Time shift) Time difference Frequency λ = c / f and c = 343 m/s at 20°C. Frequency Response.

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# Parabolic antenna

Parabolic antenna
A parabolic satellite communications antenna at Erdfunkstelle Raisting, the biggest facility for satellite communication in the world, in Raisting, Bavaria, Germany. It has a Cassegrain type feed.

A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves. The most common form is shaped like a dish and is popularly called a dish antenna or parabolic dish. The main advantage of a parabolic antenna is that it is highly directive; it functions similarly to a searchlight or flashlight reflector to direct the radio waves in a narrow beam, or receive radio waves from one particular direction only. Parabolic antennas have some of the highest gains, that is they can produce the narrowest beam width angles, of any antenna type.[1] In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used, so parabolic antennas are used in the high frequency part of the radio spectrum, at UHF and microwave (SHF) frequencies, at which wavelengths are small enough that conveniently sized dishes can be used.

Parabolic antennas are used as high-gain antennas for point-to-point communication, in applications such as microwave relay links that carry telephone and television signals between nearby cities, wireless WAN/LAN links for data communications, satellite and spacecraft communication antennas, and radio telescopes. Their other large use is in radar antennas, which need to emit a narrow beam of radio waves to locate objects like ships and airplanes. With the advent of home satellite television dishes, parabolic antennas have become a ubiquitous feature of the modern landscape.

## Design

The operating principle of a parabolic antenna is that a point source of radio waves at the focal point in front of a parabolic reflector of conductive material will be reflected into a collimated plane wave beam along the axis of the reflector. Conversely, an incoming plane wave parallel to the axis will be focused to a point at the focal point.

A typical parabolic antenna consists of a metal parabolic reflector with a small feed antenna suspended in front of the reflector at its focus, pointed back toward the reflector. The reflector is a metallic surface formed into a paraboloid of revolution and usually truncated in a circular rim that forms the diameter of the antenna. In a transmitting antenna, radio frequency current from a transmitter is supplied through a transmission line cable to the feed antenna, which converts it into radio waves. The radio waves are emitted back toward the dish by the feed antenna and reflect off the dish into a parallel beam. In a receiving antenna the incoming radio waves bounce off the dish and are focussed to a point at the feed antenna, which converts them to electric currents which travel through a transmission line to the receiver.

### Parabolic reflector

The reflector can be of sheet metal, metal screen, or wire grill construction, and it can be either a circular "dish" or various other shapes to create different beam shapes. A mesh screen reflects radio waves as well as a solid metal surface as long as the holes are smaller than 1/10 of a wavelength, so screen reflectors are often used to reduce weight and wind loads on the dish. To achieve the maximum gain, it is necessary that the shape of the dish be accurate within a small fraction of a wavelength, to ensure the waves from different parts of the antenna arrive at the focus in phase. Large dishes often require a supporting truss structure behind them to provide the required stiffness.

Wire grid-type parabolic antenna used for WLAN data link at 2.4 GHz. It transmits horizontally polarized radio waves.

A reflector made of a grill of parallel wires or bars oriented in one direction acts as a polarizing filter as well as a reflector. It only reflects linearly polarized radio waves, with the electric field parallel to the grill elements. This type is often used in radar antennas. Combined with a linearly polarized feed horn, it helps filter out noise in the receiver and reduces false returns.

### Feed antenna

The feed antenna at the reflector's focus is typically a low-gain type such as a half-wave dipole or more often a small horn antenna called a feed horn. In more complex designs, such as the Cassegrain and Gregorian, a secondary reflector is used to direct the energy into the parabolic reflector from a feed antenna located away from the primary focal point. The feed antenna is connected to the associated radio-frequency (RF) transmitting or receiving equipment by means of a coaxial cable transmission line or waveguide.

An advantage of parabolic antennas is that most of the structure of the antenna (all of it except the feed antenna) is nonresonant, so it can function over a wide range of frequencies, that is a wide bandwidth. All that is necessary to change the frequency of operation is to replace the feed antenna with one that works at the new frequency. Some parabolic antennas transmit or receive at multiple frequencies by having several feed antennas mounted at the focal point, close together.

Dish parabolic antennas

Shrouded microwave relay dishes on a communications tower in Australia.
A satellite television dish, an example of an offset fed dish.
Cassegrain satellite communication antenna in Sweden.
Offset Gregorian antenna used in the Allen Telescope Array, a radio telescope at the University of California at Berkeley, USA.

Cylindrical parabolic antennas

Vertical "orange peel" antenna for military altitude measuring radar, Germany.
Early cylindrical parabolic antenna, 1931, Nauen, Germany.
Air traffic control radar antenna, near Hannover, Germany.
"Orange peel" antenna for air search radar, Finland.

## Types

Main types of parabolic antenna feeds.

Parabolic antennas are distinguished by their shapes:

• Paraboloidal or dish - The reflector is shaped like a paraboloid. This is the most common type. It radiates a narrow pencil-shaped beam along the axis of the dish.
• Shrouded dish - Sometimes a cylindrical metal shield is attached to the rim of the dish.[2] The shroud shields the antenna from radiation from angles outside the main beam axis, reducing the sidelobes. It is sometimes used to prevent interference in terrestrial microwave links, where several antennas using the same frequency are located close together. The shroud is coated inside with microwave absorbent material. Shrouds can reduce back lobe radiation by 10 dB.[2]
• Cylindrical - The reflector is curved in only one direction and flat in the other. The radio waves come to a focus not at a point but along a line. The feed is sometimes a dipole antenna located along the focal line. Cylindrical parabolic antennas radiate a fan-shaped beam, narrow in the curved dimension, and wide in the uncurved dimension. The curved ends of the reflector are sometimes capped by flat plates, to prevent radiation out the ends, and this is called a pillbox antenna.
• "Orange peel" - Another type is very long and narrow, shaped like the letter "C". This is called an orange peel design, and radiates an even wider fan beam. It is often used for radar antennas.

They are also classified by the type of feed; how the radio waves are supplied to the antenna:[2]

• Axial or front feed - This is the most common type of feed, with the feed antenna located in front of the dish at the focus, on the beam axis. A disadvantage of this type is that the feed and its supports block some of the beam, which limits the aperture efficiency to only 55 - 60%.[2]
• Offset or off-axis feed - The reflector is an asymmetrical segment of a paraboloid, so the focus, and the feed antenna, are located to one side of the dish. The purpose of this design is to move the feed structure out of the beam path, so it doesn't block the beam. It is widely used in home satellite television dishes, which are small enough that the feed structure would otherwise block a significant percentage of the signal.
• Cassegrain - In a Cassegrain antenna the feed is located on or behind the dish, and radiates forward, illuminating a convex hyperboloidal secondary reflector at the focus of the dish. The radio waves from the feed reflect back off the secondary reflector to the dish, which forms the outgoing beam. An advantage of this configuration is that the feed, with its waveguides and "front end" electronics does not have to be suspended in front of the dish, so it is used for antennas with complicated or bulky feeds, such as large satellite communication antennas and radio telescopes. Aperture efficiency is on the order of 65 - 70%[2]
• Gregorian - Similar to the Cassegrain design except that the secondary reflector is concave, (ellipsoidal) in shape. Aperture efficiency over 70% can be achieved.[2]

## Feed pattern

The radiation pattern of the feed antenna has to be tailored to the shape of the dish, because it has a strong influence on the aperture efficiency, which determines the antenna gain (see Gain section below). Radiation from the feed that falls outside the edge of the dish is called "spillover" and is wasted, reducing the gain and increasing the backlobes, possibly causing interference or (in receiving antennas) increasing susceptibility to ground noise. However, maximum gain is only achieved when the dish is uniformly "illuminated" with a constant field strength to its edges. So the ideal radiation pattern of a feed antenna would be a constant field strength throughout the solid angle of the dish, dropping abruptly to zero at the edges. However, practical feed antennas have radiation patterns that drop off gradually at the edges, so the feed antenna is a compromise between acceptably low spillover and adequate illumination. For most front feed horns, optimum illumination is achieved when the power radiated by the feed horn is 10 dB less at the dish edge than its maximum value at the center of the dish.[3]

## History

The idea of using parabolic reflectors for radio antennas was taken from optics, where the power of a parabolic mirror to focus light into a beam has been known since classical antiquity. The designs of some specific types of parabolic antenna, such as the Cassegrain and Gregorian, come from similarly named analogous types of reflecting telescope, which were invented by astronomers during the 15th century.[4]

German physicist Heinrich Hertz constructed the world's first parabolic reflector antenna in 1888. The antenna was a cylindrical parabolic reflector made of zinc sheet metal supported by a wooden frame, and had a spark-gap excited dipole along the focal line. Its aperture was 1.2 meters wide, with a focal length of 0.12 meters, and was used at an operating frequency of about 450 MHz. With two such antennas, one used for transmitting and the other for receiving, Hertz demonstrated the existence of radio waves which had been predicted by James Clerk Maxwell some 22 years earlier.[5]

Italian radio pioneer Guglielmo Marconi used a parabolic reflector during the 1930s in investigations of UHF transmission from his boat in the Mediterranean.[4] In 1931 a microwave relay link across the English Channel using 10 ft. (3 meter) diameter dishes was demonstrated.[4] In 1934 Karl Jansky built the first radio telescope to use a parabolic antenna, and with it detected radio emissions from the Milky Way, a discovery which founded the field of radio astronomy.[4] The development of radar during World War II provided a great impetus to parabolic antenna research, and saw the evolution of shaped-beam antennas, in which the curve of the reflector is different in the vertical and horizontal directions, tailored to produce a beam with a particular shape.[4] During the 1950s dish antennas became widely used in terrestrial microwave relay communication systems.[4]

The first parabolic antenna used for satellite communications was constructed in 1962 at Goonhilly in Cornwall, England, UK to communicate with the Telstar satellite.

## Gain

The largest "dish" antenna in the world, the radio telescope at Arecibo Observatory, Puerto Rico, 1000 feet (305 meters) in diameter. It has a gain of about 10 million, or 70 dBi, at 2.38 GHz.[6] The dish is built into a valley in the landscape, so it is not steerable. To steer the antenna to point to different regions in the sky, the feed antenna suspended by cables over the dish is moved. The dish actually has a spherical rather than a parabolic shape, which reduces the aberrations caused by moving the feed point.

The directive qualities of an antenna are measured by a dimensionless parameter called its gain, which is the ratio of the power received by the antenna from a source along its beam axis to the power received by a hypothetical isotropic antenna. The gain of a parabolic antenna is:[7]

$G = \frac{4 \pi A}{\lambda^2}e_A = \frac{\pi^2d^2}{\lambda^2}e_A$

where:

• A is the area of the antenna aperture, that is, the mouth of the parabolic reflector
• d is the diameter of the parabolic reflector
• λ is the wavelength of the radio waves.
• eA is a dimensionless parameter between 0 and 1 called the aperture efficiency. The aperture efficiency of typical parabolic antennas is 0.55 to 0.70.

It can be seen that, as with any aperture antenna, the larger the aperture is, compared to the wavelength, the higher the gain. The gain increases with the square of the ratio of aperture width to wavelength, so large parabolic antennas, such as those used for spacecraft communication and radio telescopes, can have extremely high gain. Applying the above formula to the 25-meter-diameter antennas used by the VLA and VLBA radio telescopes at a wavelength of 21 cm (1.42 GHz, a common radio astronomy frequency) yields an approximate maximum gain of 140,000 times or about 50 dBi (decibels above the isotropic level).

Aperture efficiency eA is a catchall variable which accounts for various losses that reduce the gain of the antenna from the maximum that could be achieved with the given aperture. The major factors reducing the aperture efficiency in parabolic antennas are:.[8]

• Feed spillover - Some of the radiation from the feed antenna falls outside the edge of the dish and so doesn't contribute to the main beam.
• Feed illumination taper - The maximum gain for any aperture antenna is only achieved when the intensity of the radiated beam is constant across the entire aperture area. However the radiation pattern from the feed antenna usually tapers off toward the outer part of the dish, so the outer parts of the dish are "illuminated" with a lower intensity of radiation. Even if the feed provided constant illumination across the angle subtended by the dish, the outer parts of the dish are farther away from the feed antenna than the inner parts, so the intensity would drop off with distance from the center. So the intensity of the beam radiated by a parabolic antenna is maximum at the center of the dish and falls off with distance from the axis, reducing the efficiency.
• Aperture blockage - In front-fed parabolic dishes where the feed antenna is located in front of the dish in the beam path (and in Cassegrain and Gregorian designs as well), the feed structure and its supports block some of the beam. In small dishes such as home satellite dishes, where the size of the feed structure is comparable with the size of the dish, this can seriously reduce the antenna gain. To prevent this problem these types of antennas often use an offset feed, where the feed antenna is located to one side, outside the beam area. The aperture efficiency for these types of antennas can reach 0.7 to 0.8.
• Shape errors - random surface errors in the shape of the reflector reduce efficiency. The loss is approximated by Ruze's Equation.

For theoretical considerations of mutual interference (at frequencies between 2 and c. 30 GHz - typically in the Fixed Satellite Service) where specific antenna performance has not been defined, a reference antenna based on Recommendation ITU-R S.465 is used to calculate the interference, which will include the likely sidelobes for off-axis effects.

## Beamwidth

C-band Satellite dish, Bucharest, Romania

The angular width of the beam radiated by high-gain antennas is measured by the half-power beam width (HPBW), which is the angular separation between the points on the antenna radiation pattern at which the power drops to one-half (-3 dB) its maximum value. For parabolic antennas, the HPBW θ is given by:[3][9]

$\theta = k\lambda / d \,$

where k is a factor which depends on the shape of the reflector and the feed illumination pattern. For a "typical" parabolic antenna k = 70 when θ is in degrees.[9]

For a typical 2 meter satellite dish operating on C band (4 GHz), like the one shown at right, this formula gives a beamwidth of about 2.6°. For the Arecibo antenna at 2.4 GHz the beamwidth is 0.028°. It can be seen that parabolic antennas can produce very narrow beams, and aiming them can be a problem. Some parabolic dishes are equipped with a boresight so they can be aimed accurately at the other antenna.

It can be seen there is an inverse relation between gain and beam width. By combining the beamwidth equation with the gain equation, the relation is:[9]

$G = \left ( \frac{\pi k}{\theta} \right )^2 \epsilon_A$

## References

1. ^ Straw, R. Dean, Ed. (2000). The ARRL Antenna Book, 19th Ed.. USA: American Radio Relay League. pp. 19.15. ISBN 0872598179.
2. ^ a b c d e f Lehpamer, Harvey (2010). Microwave transmission networks: Planning, Design, and Deployment. USA: McGraw Hill Professional. pp. 268–272. ISBN 0071701222.
3. ^ a b Straw, R. Dean, Ed. (2000). The ARRL Antenna Book, 19th Ed.. USA: American Radio Relay League. pp. 18.14. ISBN 0872598179.
4. ^ a b c d e f
5. ^ Love, Allan W.. "Large Space Antenna Concepts for ESGP" (PDF). Rockwell International. Retrieved 2009-07-31.
6. ^ Drentea, Cornell (2010). Modern Communications Receiver Design and Technology. USA: Artech House. pp. 369. ISBN 1596933097.
7. ^ Anderson, Harry R. (2003). Fixed broadband wireless system design. USA: John Wiley & Sons. pp. 206–207. ISBN 0470844388.
8. ^ Pattan, Bruno (1993). Satellite systems: principles and technologies. USA: Springer. pp. 267. ISBN 0442013574.
9. ^ a b c Minoli, Daniel (2009). Satellite Systems Engineering in an IPv6 Environment. USA: CRC Press. pp. 78. ISBN 1420078682.

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### Look at other dictionaries:

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• Parabolic mirror — Parabolic Par a*bol ic, Parabolical Par a*bol ic*al, a. [Gr. paraboliko s figurative: cf. F. parabolique. See {Parable}.] [1913 Webster] 1. Of the nature of a parable; expressed by a parable or figure; allegorical; as, parabolical instruction.… …   The Collaborative International Dictionary of English

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• parabolic — parabolic1 [par΄ə bäl′ik] adj. [LL parabolicus < LGr parabolikos] of, in the form of, or expressed by a parable: also parabolical parabolically adv. parabolic2 [par΄ə bäl′ik] adj. 1. of or like a parabola 2. bowl shaped, as a reflector,… …   English World dictionary


text:
# Image of regular submanifold is a regular/embedded submanifold.

Let $$F:N\rightarrow M$$ be a smooth embedding. Then, $$F(N)$$ is an embedded submanifold of $$M$$.

So what I have tried is the following: Let $$F(p)\in F(N)$$ for some $$p\in N$$. As $$F$$ is an immersion, by the immersion theorem, there exists charts $$(U,\phi)=(U,x^1,....,x^n)$$ about $$p$$ and $$(V,\psi)=(V,y^1,.....,y^m)$$ about $$F(p)$$ on which $$F(U)\subseteq V$$ and $$(\psi \circ F\circ \phi^{-1})(x^1,.....,x^n)=(x^1,.....,x^n,0,.....,0)$$ on $$\phi(U)$$.

As $$F(N)$$ is homeomorphic to $$N$$, there exists an open set $$W$$ in $$M$$ such that $$F(U)=V'\cap F(N)$$. Hence, $$V\cap V'\cap F(N)= V\cap F(U)=F(U)$$.

Claim: $$\psi(V\cap V'\cap F(N))$$ = $$\psi(V\cap V')\cap (\mathbb{R}^{n}$$ $$\times \{0\} )$$

Now clearly, $$\subseteq$$ holds. However, I don't think the reverse inclusion holds. I mean, for $$\psi(q)\in \psi(V\cap V') \cap (\mathbb{R}^n \times \{0\})$$ , there is no immediate reason for $$q$$ to be in $$F(N)$$ as well.

To remedy this situation, I suppose we would need to construct a new chart $$W$$ such that $$W\subseteq V\cap V'$$ and $$W\subseteq F(N)$$. I would like a nudge in the right direction.

• Improve your question: state that you want to prove a statement, then give the statement (as a proposition for instance) then recall the definition of smooth embedding and embedded submanifold, then only give your attempts. – Arnaud Oct 7 '20 at 16:38

The inclusion $$\psi(V\cap V'\cap F(N))\subseteq\psi(V\cap V')\cap (\mathbb{R}^{n}\times \{0\} )$$ could indeed be strict, but note that if dim$$(N)$$<dim$$(M)$$ restricting the chart $$(V,\psi)$$ to some open set $$W$$ with $$W\subseteq F(N)$$ cannot work for dimensional reasons.
$$W=V\cap V'\cap \psi^{-1}(\phi(U)\times\mathbb R^{m-n})$$
This ensures that in addition the ''$$\mathbb R^n$$-part" in the image of $$\psi$$ only comes from points in the domain of $$\phi$$. More formally, as an injection $$\psi$$ respects intersections, so $$\psi(W)\cap(\mathbb R^n\times\{0\}) =\psi(V\cap V')\cap(\phi(U)\times\mathbb R^{m-n})\cap (\mathbb R^n\times\{0\}) =\psi(V\cap V')\cap(\phi(U)\times\{0\}) =\psi(V\cap V')\cap\psi(F(U)) =\psi(V\cap V'\cap F(N))$$ and intersecting both sides with $$\psi(W)$$ yields
$$\psi(W)\cap(\mathbb R^n\times\{0\})=\psi(W\cap F(N))$$


text:
MathSciNet bibliographic data MR1693919 62H25 Ten Berge, Jos M. F.; Kiers, Henk A. L. Simplicity of core arrays in three-way principal component analysis and the typical rank of $p\times q\times 2$$p\times q\times 2$ arrays. Linear Algebra Appl. 294 (1999), no. 1-3, 169–179. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
Precalculus (6th Edition) Blitzer

Put the equal symbol in place of the inequality symbol: Now, the equation is ${{\left( x-2 \right)}^{2}}+{{\left( y-4 \right)}^{2}}=9$. For a circle having center $\left( h,k \right)$ and radius $r$, the general equation of the circle is ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$. So, the equation ${{\left( x-2 \right)}^{2}}+{{\left( y-4 \right)}^{2}}=9$ can be represented as ${{\left( x-2 \right)}^{2}}+{{\left( y-4 \right)}^{2}}={{3}^{2}}$ Thus, the center of the circle $\left( h,k \right)=\left( 2,4 \right)$ and radius $r=3$. To plot this circle in the rectangular coordinate system, consider $\left( 2,4 \right)$ as the origin and draw a circle taking radius $r=3$. Now, this circle divides the plane into three regions: the circle itself, the inner plane of the circle, and the outer plane of the circle. Now, consider a test point $\left( 0,0 \right)$ and check whether the test point satisfies the inequality ${{\left( x-2 \right)}^{2}}+{{\left( y-4 \right)}^{2}}>9$ \begin{align} {{\left( 0-2 \right)}^{2}}+{{\left( 0-4 \right)}^{2}}\overset{?}{\mathop{>}}\,9 & \\ 4+16\overset{?}{\mathop{>}}\,9 & \\ 20>9 & \\ \end{align} It is correct. Therefore, the test point satisfies the inequality, so we shade the plane containing the test point and draw the circle with a dotted line as it contains only the greater-than sign. Thus, the graph of this inequality is the shaded region.


text:
# Useful pairings for cryptography

I've recently looked a bit at pairing based cryptography and I was wondering what properties the groups involved should have in order to be useful for cryptographic purposes? Has anything more exact been formulated? As an example, we could just take the pairing

$\mathbb{Z}_p\times \mathbb{Z}_p\to \mathbb{Z}_p,\;\; (x,y)\mapsto xy,$

where the group is the additive subgroup of $\mathbb{Z}_p$. Clearly, this would not be terribly useful for cryptographic applications, since picking any nonzero $a\in \mathbb{Z}_p$ as a generator, we can trivially solve the discrete logatithm problem in this additive group. Hence any standard formulation of Diffie-Hellman can be solved as $c$ from $ca$ can be solved just by multiplying with the inverse of $a$, which is efficiently computable. How do we differentiate between ''good'' and ''bad'' groups?

-

That depends on the protocol being used, but most pairing-based protocols assume that the Bilinear Diffie-Hellman (BDH) problem is hard: given $P, aP, bP, cP$ for group element $P$ and integers $a, b, c$ it is hard to compute $e(P, P)^{abc}$ for a given pairing $e$.

There are many related problems that, if broken, could be used to break the BDH: the discrete logarithm, the Computational Diffie-Hellman (given $P, aP, bP$ compute $abP$), etc.

-
Thanks. My question might have been a bit vague, but I was sort of thinking about whether there's some sort of fuzzy classification of such groups where this is assumed to be hard. In other words, what properties the groups should NOT have for the various Diffie-Hellman problems to be assumed difficult. Knowing how little one knows about complexities of hard problems in general, I assume that this is unknown. –  del Apr 26 '12 at 16:00
@EdvardFagerholm, unless you can somehow narrow down the question somehow, I don't think you're going to get a more useful answer than the characterization "groups where the BDH problem is hard". I don't think we have a complete characterization of what groups the BDH problem is hard in, based solely upon clean/elementary properties of the group. –  D.W. May 1 '13 at 20:40


text:
Thread: Need help with this limit!

1. Need help with this limit!

$\lim_{x\to0^+}(9x+1)^{cotx}$

Hopefull I am at least on the right track, here's what I tried to do:

Let $y=(9x+1)^{cotx}$

$\lim_{x\to0^+}lny=cot(x)ln(9x+1)$

$\lim_{x\to0^+}lny=\frac{ln(9x+1)}{\frac{1}{cot(x)} }$

$\lim_{x\to0^+}lny=\frac{\frac{9}{9x+1}}{\frac{csc^ 2x}{cot^2x}}$

And I don't know what to do next.

2. Originally Posted by xxlvh
$\lim_{x\to0^+}(9x+1)^{cotx}$

Hopefull I am at least on the right track, here's what I tried to do:

Let $y=(9x+1)^{cotx}$

$\lim_{x\to0^+}lny=cot(x)ln(9x+1)$

$\lim_{x\to0^+}lny=\frac{ln(9x+1)}{\frac{1}{cot(x)} }$

$\lim_{x\to0^+}lny=\frac{\frac{9}{9x+1}}{\frac{csc^ 2x}{cot^2x}}$

And I don't know what to do next.
note that $\frac 1{\cot x} = \tan x$. The derivative is $\sec^2 x$ (if you simplified your denominator, you would have gotten the same thing). Now just plug in $x = 0$ and continue

(You should have the $\lim_{x \to 0^+}$ on the right side of the equation also)


text:
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Get Full Access to Chemistry: Structure And Properties - 2 Edition - Chapter 22 - Problem 75
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ISBN: 9780134293936 2043

## Solution for problem 75 Chapter 22

Chemistry: Structure and Properties | 2nd Edition

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Problem 75

Halide complexes of metal M of the form $$\left[\mathrm{MX}_{6}\right]^{3-}$$ are found to be stable in aqueous solution. But it is possible that they undergo rapid ligand exchange with water (or other ligands) that is not detectable because the complexes are less stable. This property is referred to as their lability. Suggest an experiment to measure the lability of these complexes that does not employ radioactive labels.

Text Transcription:

[MX_6]^3-

Step-by-Step Solution:
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Chemistry 1411 Notes 08/27/18 Measurement Quantitative Observation Has two parts – number and unit  Number tells comparison  Unit tells scale The number is meaningless without the unit Proper aspirin dosage – 325 (milligrams or pounds) Scientific notation Expresses a number as a product of a number between 110 and the appropriate power of 10 93,000,000 = 9.3 x 10,000 = 9.3 x 10^7 If the decimal point is moved to the left, the power of 10 is positive 345 = 3.45 x 10^2 If the decimal point is moved to the right, the power of 10 is negative 0.0671 = 6.71 x 10^2 2,500 = 2.5 x 10^3 0.036 = 3.6 x 10^2 Converting a number in scientific notation to a standard number When the exponent x is positive, move the decimal point x places to the right 2.800 x 10^2 = 280 Nature of Measurement Quantitate observation consisting of two parts CHEMISTRY 1411 NOTES 09/07/18 Average atomic mass  Because of the existence of isotopes, the mass of a collection of atoms has an average value.  Boron is 20% 10B and 80% 11B. That is, 11B is 80 percent abundant on earth For Boron mass = 0.20 (10 amu) +0.80 (11 amu) = 10.8 amu Elements and the periodic table The elements in the periodic tale are divided into three groups – metals, nonmetals, and semimetals Metals: - They are located on the left side of the periodic table - They are good conductors of heat and electricity - Metals are shiny solids at room temper

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##### ISBN: 9780134293936

Chemistry: Structure and Properties was written by Aimee Notetaker and is associated to the ISBN: 9780134293936. The answer to “?Halide complexes of metal M of the form $$\left[\mathrm{MX}_{6}\right]^{3-}$$ are found to be stable in aqueous solution. But it is possible that they undergo rapid ligand exchange with water (or other ligands) that is not detectable because the complexes are less stable. This property is referred to as their lability. Suggest an experiment to measure the lability of these complexes that does not employ radioactive labels.Text Transcription:[MX_6]^3-” is broken down into a number of easy to follow steps, and 67 words. Since the solution to 75 from 22 chapter was answered, more than 203 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 75 from chapter: 22 was answered by Aimee Notetaker, our top Chemistry solution expert on 04/25/22, 03:51PM. This textbook survival guide was created for the textbook: Chemistry: Structure and Properties, edition: 2. This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 130 solutions.

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