text:
5

## Question

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##### MatnticomMath 135-03 (1)omework: 11.2 IA'reparing for Section 11.2 IntroductionObjectiveObjectiveObjective jest Hypotheses tor Population Haan from MatcneoIntcrence ejcul 74j Pocuijticn Mean DcpendentMP ES0.29of 1 Point11.210-TAresearcher sludies waler danty at the same location = Iake on tne san # dates dunng tho course 01a year and rep weighted disk painted Dack and white and measures the dcplh (in inches) at wtich it Is Jorgof visible; Tie &ec Obsenrtion 1/25 319 9/13 Inttial Depih
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text:
# Measuring Transmission Time¶

## Goals¶

In this example we explore the packet transmission time statistics of network interfaces for wired and wireless transmission mediums.

INET version: 4.4

## The Model¶

The packet transmission time is measured from the moment the beginning of the physical signal encoding the packet leaves the network interface up to the moment the end of the same physical signal leaves the same network interface. This time usually equals with the packet reception time that is measured at the receiver network interface from the beginning to the end of the physical signal. The exception would be when the receiver is moving relative to the transmitter with a relatively high speed compared to the propagation speed of the physical signal, but it is rarely the case in communication network simulation.

Packet transmission time is measured from the beginning of the physical signal encoding the packet leaves the network interface up to the moment the end of the same physical signal leaves the same network interface.

Packet transmission time is the time difference between the start and th end of the physical signal transmission on the outgoing interface.

Here is the network:

Here is the configuration:

[General]
network = TransmissionTimeMeasurementShowcase
description = "Measure packet transmission time on the channel"
sim-time-limit = 1s

# source application ~96Mbps throughput
*.source.numApps = 1
*.source.app[0].typename = "UdpSourceApp"
*.source.app[0].source.packetLength = int(truncnormal(800B, 200B))
*.source.app[0].source.productionInterval = exponential(100us)
*.source.app[0].io.destPort = 1000

# destination application
*.destination.numApps = 1
*.destination.app[0].typename = "UdpSinkApp"
*.destination.app[0].io.localPort = 1000

# enable modular Ethernet model
*.*.ethernet.typename = "EthernetLayer"
*.*.eth[*].typename = "LayeredEthernetInterface"

# data rate of all network interfaces
*.*.eth[*].bitrate = 100Mbps

## Results¶

TODO should the packet length be variable ? so the transmission time is not the same

Here are the results:

## Discussion¶

Use this page in the GitHub issue tracker for commenting on this showcase.

format: plain


text:
# Homogeneous equilibrium model-fluid flow

Tags:
1. Jun 5, 2015

### Sivaraman

Hello,I am trying to calculate the velocity in a pipe with length L and Dia D, which is connected to bottom of a pressurized vessel (Vessel dimensions are known, Level of liquid inside the vessel is known).
Now i need to figure out the velocity as a function of pressure inside the vessel.We can ignore the friction losses in the pipe, and the vessel is filled with water. Thank you

Last edited: Jun 5, 2015
2. Jun 10, 2015


text:
## Saturday, July 15, 2017

### Maryam Mirzakhani, RIP

This news is really tragic because the death is truly premature.

Maryam Mirzakhani, the world's first female Fields Medal winner and Persia's first winner of that award, died of breast cancer at an American hospital today. The disease was recurrent and things became terrible when the disease spread to the bone marrow.

She was born in 1977 to parents who always supported her even though they weren't ever too ambitious, she once told me. Her father Ahmad is an electrical engineer. Maryam is also survived by her Czech husband Jan Vondrák, a computer scientist at Stanford and their daughter Anahita (*2011). For a while, we were (theoretical physics!) classmates in Prague with him in late 1994 and/or early 1995 and he we overlapped at Rutgers (in different dpts) in 1999-2001.

Maryam was born in Tehran in May 1977. As a kid, she wanted to write fiction novels. She was talented so they accepted her to a high school for exceptionally talented students, the "NODET" network, in Farzanegan. Sometime at that moment, someone pointed out to her that she was really good in mathematics. Her maturing as a mathematician looked automatic since that time. Both in 1994 and 1995, she won gold medals at the International Mathematical Olympiad, the second one was with a perfect score.

In 1999, she got her BSc from Sharif "MIT" in Tehran. Then she studied her PhD at Harvard when I was a Junior Fellow there. Curtis McMullen – a Fields medalist – was her adviser. She finally got her PhD in 2004. She was immediately offered an easier access to the Harvard Society of Fellows so we talked to her during several fancy dinners. Well, I think that I was sitting next to her during all these occasions. I think it's right to say that she was a modest and shy genius, perhaps somewhat resembling Juan Maldacena in some respects.

She refused the offer to become a junior fellow because she had something that ultimately looks better than even the best postdoc-like jobs. In 2004, she accepted a junior faculty position at Princeton while she was also a research fellow at the Clay Mathematics Institute. The jobs probably overlapped. Now, her salary as junior faculty at Princeton almost certainly trumped the salary of the Harvard Junior Fellows but if I were making this decision today, with everything I know, I would surely choose the Harvard Junior Fellowship at that time. At any rate, soon afterwards, she soon moved from Princeton to Stanford where she met her Czech husband – a move that physicists refer to as a solution to the two-body problem.

She received the 2014 Fields Medal as the first woman. It may be estimated that under meritocratic conditions, a woman wins this medal once in 103 years or so. Her medal was mostly for her work on the moduli spaces of Riemann surfaces, especially for her 2007 proof of a formula for volumes of the moduli spaces (previously conjectured by Witten, Kontsevich, guys of this caliber are normal in that field). However, she has done lots of related mathematical work that was usually focusing on the modular group, moduli spaces, and geodesics – which were sometimes shown to be ergodic, sometimes very regular and not chaotic, and similar issues were relevant.

I believe that in general, breast cancer is overdiagnosed and most of the women who undergo a treatment would do just OK without it. Sometimes, sadly, the diagnosis is so spot on that even a treatment isn't enough. Czech singer Anna K was just diagnosed with breast cancer for the second time. She plans to fight it by a string of concerts throughout the summer.

RIP, Maryam.


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# 32

Personal Blog

I'm pleased to announce a new paper from MIRI: Formalizing Two Problems of Realistic World Models.

Abstract:

An intelligent agent embedded within the real world must reason about an environment which is larger than the agent, and learn how to achieve goals in that environment. We discuss attempts to formalize two problems: one of induction, where an agent must use sensory data to infer a universe which embeds (and computes) the agent, and one of interaction, where an agent must learn to achieve complex goals in the universe. We review related problems formalized by Solomonoff and Hutter, and explore challenges that arise when attempting to formalize analogous problems in a setting where the agent is embedded within the environment.

This is the fifth of six papers discussing active research topics that we've been looking into at MIRI. It discusses a few difficulties that arise when attempting to formalize problems of induction and evaluation in settings where an agent is attempting to learn about (and act upon) a universe from within. These problems have been much discussed on LessWrong; for further reading, see the links below. This paper is intended to better introduce the topic, and motivate it as relevant to FAI research.

The (rather short) introduction to the paper is reproduced below.

An intelligent agent embedded in the real world faces an induction problem: how can it learn about the environment in which it is embedded, about the universe which computes it? Solomonoff (1964) formalized an induction problem faced by agents which must learn to predict an environment which does not contain the agent, and this formalism has inspired the development of many useful tools, including Kolmogorov complexity and Hutter's AIXI. However, a number of new difficulties arise when the agent must learn about the environment in which it is embedded.

An agent embedded in the world also faces an interaction problem: how can an agent learn to achieve a complex set of goals within its own universe? Legg and Hutter (2007) have formalized an intelligence measure" which scores the performance of agents on which learn about and act upon an environment that does not contain the agent, but again, new difficulties arise when attempting to do the same in a naturalized setting.

This paper examines both problems. Section 2 introduces Solomonoff's formalization of an induction problem where the agent is separate from the environment, and Section 3 discusses troubles that arise when attempting to formalize the analogous naturalized induction problem. Section 4 discusses Hutter's interaction problem, and Section 5 discusses an open problem related to formalizing an analogous naturalized interaction problem.

Formalizing these problems is important in order to fully understand the problem faced by an intelligent agent embedded within the universe: a general artificial intelligence must be able to learn about the environment which computes it, and learn how to achieve its goals from inside its universe. Section 6 concludes with a discussion of why a theoretical understanding of agents interacting with their own environment seems necessary in order to construct highly reliable smarter-than-human systems.

# 32

New Comment

Two things that could very well come out of misunderstandings of the material:

1. If we have an agent whose actions affect future observations, why can’t we think of information about the agent’s embedding in the environment as being encoded in its observations? For example, in the heating-up game, we could imagine a computer that has sensors that detect heat emanating from its hardware, and that the data from those sensors is incorporated into the input stream of observations of the “environment”. The agent could then learn from past experience that certain actions lead to certain patterns of observations, which correspond to what people seem to mean when they say that it is giving off a certain amount of heat. We humans have a causal model in which those patterns in the computer’s observations are coming specifically from patterns in the data from specific sensors, which are triggered by the computer giving off heat, which are caused by those actions. A computer could well have an internal representation of a similar causal model, but that seems to me like part of a specific solution to the same general problem of predicting future observations and determining future actions given past observations and past actions. Even if an agent reconfigures its sensors, say, taking over every camera and microphone it can get control of over the internet, that new configuration of sensors will just get incorporated into the stream of observations, and it can “know” what it’s doing by predicting abrupt shifts in various properties of the observation stream.

2. It makes sense to me that modeling rewards as exogenously incorporated into observations doesn’t account for the possibility of specific predetermined values. But doesn’t the agent ultimately need to make decisions based purely on the information contained in its observations? We might externally judge the agent’s performance according to values that we have that depend on more information than the agent has access to, but if the ultimate goal is to program an agent to make decisions based on specific values, those values need to be at least approximated based purely on information the agent has, and we may as well define the values to be the approximation on which the agent bases its decisions. This absolutely makes it possible that under the vast majority of value systems the most “effective” agents would be ones that take over their inputs, but I think it makes sense in that case to say that those are the wrong value systems, rather than that the agent is ineffective. This doesn’t get rid of any of the ontological issues, it just shifts the burden of dealing with them to the definition of the value system, rather than to the fundamental setup of the problem of inductively optimizing an interaction, where it seems to me that the value system can be a parameter of the problem in an unambiguous way:

We define a value system, V, to be a function that takes in a finite partial history of observations and actions and outputs an incremental reward. For a given agent A and environment M, the incremental reward under value system V would be $r^{M,A,V}_t = V(M^A_{\prec = t}, A^M_{\prec t})$, with total reward $R_{M,V}(A) = \sum_{1}^{\lceil M \rceil}r^{M,A,V}_t$ used to score the agent relative to this value system (where we limit our consideration to value systems where this necessarily converges for all environments and agents). Then we could measure the effectiveness of agent A relative to value system V as $\sum_{M \in \mathcal{T}}2^{-\langle M \rangle}R_{M,V}(A)$.

1. It's useful to think of the task as one of defining the intended intelligence metric. The Legg-Hutter metric can't represent a heating-up game, because there isn't a "heat" channel from the agent to the environment. Is it possible that an agent with high Legg-Hutter intelligence might be able to succeed on the heating up game, given a heat channel? Yes, this is possible. But AIXItl would almost certainly not be able to do this (it cannot consider limiting computation for a few timesteps), and you shouldn't expect agents with high LH score to do this, because this isn't what LH measures. Embedding an agent with high LH score in a heating up game violates an assumption under which the agent was shown to behave well. The problem here is not this one game in particular, the problem is that we still don't know how to define the actual (naturalized) intelligence metric we care about. If we could formalize a set of universes and an embedding rule that allows us to measure agents on problems where their physical embodiment matters, that would constitute progress.
2. You're correct that the agent ultimately needs to choose based purely on information from its observations (well, that and the priors), but there's a difference between agents that are attempting to optimize what they see, and agents that are attempting to optimize what actually happened. Yes, the latter is ultimately an observation-based decision process, but it's a fairly complicated one (note the difficulty of cashing out the word "actually" and the need to worry about the agent's beliefs and their accuracy). The problem of ontology identification is not one of avoiding the fact that the agent must decide based on observations "alone", it's one of figuring out how to build agents that do the specific type of observation-based decision that we prefer (e.g. optimizing for reality rather than sense data). The real question, after all, is "we want agents that optimize actual reality, how do we build them?" -- this requires cashing out some parts of the question that are glossed over if you define environments as "a thing that spits out an observation and a reward in each timestep."

With regards to your suggestion of a metric which allows the value function to vary, this is all well and good, but now how do I find the V that actually corresponds to my goals? Say I want the V which scores the agent well for maximizing diamond in reality. This requires specifying a function which (1) takes observations; (2) uses them along with priors and knowledge about how the agent behaves to compute the expected state of outside reality; and (3) computes how much diamond is actually in reality and scores accordingly. But that's not a value function, that's most of an AGI!

It's fine to say that the utility function must ultimately be defined over percepts, but in order to give me the function over percepts that I actually want (e.g. one that figures out how reality looks and scores an agent for maximizing it appropriately), I need a value function which turns percepts into a world model, figures out what the agent is going to do, and solves the ontology identification problem in order to rate the resulting world history. A huge part of the problem of intelligence is figuring out how to define a function of percepts which optimizes goals in actual reality -- so while you're welcome to think of ontology identification as part of "picking the right value function", you eventually have to unpack that process, and the ontology identification problem is one of the hurdles that arises when you try to do so.

I hope that helps!

[-][anonymous]6y 0

This absolutely makes it possible that under the vast majority of value systems the most “effective” agents would be ones that take over their inputs, but I think it makes sense in that case to say that those are the wrong value systems, rather than that the agent is ineffective.

Certainly the agent is ineffective. It destroyed information which could have reduced its value-uncertainty.

Suppose that instead of having well-defined actions AIXI only has access to observables and its reward function. It might seem hopeless, but consider the subset of environments containing an implementation of a UTM which is evaluating T_A, a Turing machine implementing action-less AIXI, in which the implementation of the UTM has side effects in the next turn of the environment. This embeds AIXI-actions as side effects of an actual implementation of AIXI running as T_A on a UTM in the set of environments with observables matching those that the abstract AIXI-like algorithm observes. To maximize the reward function the agent must recognize its implementation embedded in the UTM in M and predict the consequences of the side effects of various choices it could make, substituting its own output for the output of the UTM in the next turn of the simulated environment (to avoid recursively simulating itself), choosing the side effects to maximize rewards.

In this context counterfactuals are simulations of the next turns of M resulting from the possible side effects of its current UTM. To be useful there must be a relation from computation-suffixes of T_A to the potential side effects of the UTM. In other words the agent must be able to cause a specific side effect as a result of state-transitions or tape operations performed causally-after it has determined which side effect will maximize rewards. This could be as straightforward as the UTM using the most-recently written bits on the tape to choose a side effect.

In the heating game, the UTM running T_A must be physically implemented as something that has a side effect corresponding to temperature, which causally effects the box of rewards, and all these causes must be predictable from the observables accessible to T_A in the UTM. Similarly, if there is an anvil suspended above a physical implementation of a UTM running T_A, the agent can avoid an inability to increase rewards in the future of environments in which the anvil is caused to drop (or escape from the UTM before dropping it).

This reduces the naturalized induction problem to the tiling/consistent reflection problem; the agent must choose which agent it wants to be in the next turn(s) through side effects that can change its future implementation.

Thanks for the comments, this is an interesting line of reasoning :-)

An AIXI that takes no actions is just a Solomonoff inductor, and this might give you some intuition for why, if you embed AIXI-without-actions into a UTM with side effects, you won't end up with anything approaching good behavior. In each turn, it will run all environment hypotheses and update its distribution to be consistent with observation -- and then do nothing. It won't be able to "learn" how to manage the "side effects"; AIXI is simply not an algorithm that attempts to do any such thing.

You're correct, though, that examining a setup where a UTM has side effects (and picking an algorithm to run on that UTM) is indeed a way to examine the "naturalized" problems. In fact, this idea is very similar to Orseau and Ring's space-time embedded intelligence formalism. The big question here (which we must answer in order to be able to talk about which algorithms "perform well") is what distribution over environments an agent will be rated against.

In this context counterfactuals are simulations of the next turns of M resulting from the possible side effects of its current UTM.

I'm not exactly sure how you would formalize this. Say you have a machine M implemented by a UTM which has side effects on the environment. M is doing internal predictions but has no outputs. There's this thing you could do which is predict what would happen from running M (given your uncertainty about how the side effects work), but that's not a counterfactual, that's a prediction: constructing a counterfactual would require considering different possible computations that M could execute. (There are easy ways to cash out this sort of counterfactual using CDT or EDT, but you run into the usual logical counterfactual problems if you try to construct these sorts of counterfactuals using UDT, as far as I can tell.)

This reduces the naturalized induction problem to the tiling/consistent reflection problem; the agent must choose which agent it wants to be in the next turn(s) through side effects that can change its future implementation.

Yeah, once you figure out which distribution over environments to score against and how to formalize your counterfactuals, the problem reduces to "pick the action with the best future side effects", which throws you directly up against the Vingean reflection problem in any environment where your capabilities include building something smarter than you :-)


text:
# XAML Aesthetics: Value Converters

• Tutorial

This article presents generalized approaches for using value converters into writing of XAML code.

IValueConverter Data Binding XAML WPF UWP Xamarin Forms UI SwitchConverter KeyToValueConverter InlineConverter AggregateConverter ResourceDictionary

Value converters together with a data binding mechanism are essential components into XAML-based development of user interfaces. Value converters imply the presence of logic placed in a separated class that implements the IValueConverter interface. Typically, the class name reflects the functional purpose, and the instances are declared in the markup.

Switch Converter & Key To Value Converter

At practice many value converters have trivial logic similar by structure with ternary operator (? :) or if-else, switch-case-default constructions. However, there are generalized patterns KeyToValueConverter and SwitchConverter, which allow to avoid adding to the project of similar by structure classes via declaring logical values and branches directly into markup.

Conception

<KeyToValueConverter
Key="KeyForMatching"
Value="ValueIfKeyMatched"
ByDefault="ValueIfKeyNotMatched" />

<SwitchConverter
ByDefault="ValueZ">
<Case
Key="KeyA"
Value="ValueA" />
<Case
Key="KeyB"
Value="ValueB" />
<Case
Key="KeyC"
Value="ValueC" />
</SwitchConverter>

Usage

<KeyToValueConverter
x:Key="TrueToVisibleConverter"
Key="True"
Value="Visible"
ByDefault="Collapsed" />

<ProgressBar
Visibility="{Binding IsBusy, Converter={StaticResource TrueToVisibleConverter}}" />

<SwitchConverter
x:Key="CodeToBackgroundConverter"
ByDefault="White">
<Case
Key="R"
Value="Red" />
<Case
Key="G"
Value="Green" />
<Case
Key="B"
Value="Blue" />
</SwitchConverter>

<Control
Background="{Binding Code, Converter={StaticResource CodeToBackgroundConverter}}" />

KeyToValueConverter - checks the input value for compliance with the value from the Key property, if the match is met, then the value from the Value property is taken as the output, otherwise from the ByDefault property.

SwitchConverter - searches for the first matching Case from the list by its key from the Key property, if the corresponding Case is found, then the value specified in it from the Value property is taken, otherwise from the ByDefault property, specified in the converter itself.

If the property Value orByDefault is not explicitly set, but the corresponding condition is satisfied, then in this case, an ordinary forwarding of the input value as an output occurs.

Also, it is sometimes useful for KeyToValueConverter to set a key in ConverterParameter via the KeySource property

<KeyToValueConverter
x:Key="EqualsToHiddenConverter"
KeySource="ConverterParameter"
Value="Collapsed"
ByDefault="Visible" />

<Control
Visiblity="{Binding Items.Count, ConverterParameter=0, Converter={StaticResource EqualsToHiddenConverter}}" />

<TextBlock
Visiblity="{Binding Text, ConverterParameter='Hide Me', Converter={StaticResource EqualsToHiddenConverter}}" />

There are four work modes of KeySource for special cases:

Manual (by default) -  the value from the Key property is always used as a key during matching, or the value is forwarded when it is not set

ConverterParameter -  the value from the binding's property ConverterParameter is always used as the key during matching, or the value is passed through when it is not set

PreferManual - if manual Key is explicitly set, it takes precedence over ConverterParameter

PreferConverterParameter - if ConverterParameter is explicitly set, then it takes precedence over manual Key

Note that SwitchConverter, in addition to the usual Case, also has TypedCase, the main difference of which is matching by value type

<SwitchConverter
ByDefault="Undefined value">
<TypedCase
Key="system:String"
Value="String value" />
<Case
Key="0"
Value="Zero" />
<Case
Key="1"
Value="One" />
<TypedCase
Key="system:Int32"
Value="Int32 value" />
</SwitchConverter>

Sometimes it becomes necessary to debug the value converter. For this purpose, SwitchConverter has a DiagnosticKey property, if it is been set, then when the data binding is been triggered, diagnostic messages of the following format will be displayed in Trace

var diagnosticMessage = matchedCase.Is()
? $"{DiagnosticKey}: '{matchedValue}' matched by key '{matchedCase.Key}' for '{value}' and converted to '{convertedValue}'" :$"{DiagnosticKey}: The default value '{matchedValue}' matched for '{value}' and converted to '{convertedValue}'";

Trace.WriteLine(diagnosticMessage);
<SwitchConverter
DiagnosticKey="UniqDiagnosticKey"
x:Key="CodeToBackgroundConverter"
ByDefault="White">
...
</SwitchConverter>

Dependency Value Converter

It is also useful to declare Key, Value and ByDefault properties as Dependency Properties, that means inheritance of converters and Cases from the DependencyObject class. Although value converters are usually not elements of the visual tree, which partly limits the work of the data binding mechanism, nevertheless, it remains possible to bind to static resources or descendants of the Binding class, for example

<KeyToValueConverter
Key="AnyKey"
Value="{Binding MatchedValue, Source={StaticResource AnyResource}}"
ByDefault="{Binding DefaultValue, Source={StaticResource AnyResource}}" />

<KeyToValueConverter
Key="AnyKey"
Value="{Localizing MatchedTitle}"
ByDefault="{Localizing DefaultTitle}" />

Inline Converter

Inline Converter allow to transfer the values conversion logic from a separate class that implements the IValueConverter interface into the code-behind class of a concrete view based on the event model.

This allows to access the view and its individual visual elements from the conversion logic during implementation of complex scenarios that are difficult to implement with the classical approach.

To do this, you need to add the converter declaration to the markup, and into the code-behind class define handlers for the corresponding Converting and ConvertingBack events

<Grid>
<Grid.Resources>
<InlineConverter
x:Key="ComplexInlineConverter"
Converting="InlineConverter_OnConverting"
ConvertingBack="InlineConverter_OnConverting" />
</Grid.Resources>

<TextBlock
Text="{Binding Number, Converter={StaticResource InlineConverter}}" />
</Grid>
private void InlineConverter_OnConverting(object sender, ConverterEventArgs e)
{
// this.DataContext - access to Data Context or another properties of the view
e.ConvertedValue = // set output value
\$"DataContext: {DataContext}, Converter Value: {e.Value}";
}

private void InlineConverter_OnConvertingBack(object sender, ConverterEventArgs e)
{
// ...
}

Aggregate Converter

Aggregate converter intends for combining converters into chains, while the value is converted sequentially in the order in which nested converters are declared.

<AggregateConverter>
<StepAConverter />
<StepBConverter />
<StepCConverter />
</AggregateConverter>

App.xaml

It is useful to locate generic value converters in a separate Resource Dictionary and then merge them as global resources into the App.xaml file. This allows to reuse value converters in different views without re-declaring them.

<Application
xmlns="http://xamarin.com/schemas/2014/forms"
xmlns:x="http://schemas.microsoft.com/winfx/2009/xaml"
x:Class="Any.App">
<Application.Resources>
<ResourceDictionary>
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary
Source="AppConverters.xaml" />
...
</ResourceDictionary.MergedDictionaries>
</ResourceDictionary>
</Application.Resources>
</Application>

Ace Framework

Examples of implementation of the presented converters can be found into the Ace Framework library gitlab bitbucket

With gratitude for your attention and interest!


text:
0.10 Lecture 11:sinusoidal steady-state (sss) or frequency response  (Page 4/5)

Two-minute miniquiz problem

Problem 6-1

Given

$H\left(s\right)=\frac{s}{\left(s+1\right)\left(s+\text{10}\right)}$

Determine the magnitude of the frequency response in the form of a Bode diagram.

Solution

$H\left(\mathrm{j\omega }\right)=\frac{1}{\text{10}}\left[\frac{\mathrm{j\omega }}{\left(\mathrm{j\omega }+1\right)\left(\mathrm{j\omega }/\text{10}+1\right)}\right]$

V. SIGNAL PROCESSING WITH FILTERS

1/ Separation of narrowband signals

The input consists of a sum of two sinusoids, more generally the sum of two narrow-band signals such as the signals transmitted by two radio stations. The objective is to devise filters

to separate these two signals. All waveforms have normalized amplitudes.

2/ Extraction of narrow-band signal from wide-band noise

The input consists of a sinusoid, more generally a narrow-band signal, plus some wide-band noise. The objective is to extract the signal from the noise. All waveforms have normalized amplitudes.

3/ Reduction of narrow-band noise from wide-band signal

The input consists of a wide-band signal, in this case an ecg signal recorded from the surface of the chest, plus some narrowband noise, such as pickup from the power lines. The objective is to remove the narrow-band noise. All waveforms have normalized amplitudes.

VI. LOWPASS AND HIGHPASS FILTERS

1/ First-order lowpass and highpass filters

where H(s) = Y (s)/X(s) and RC = 1.

2/ Use of first-order lpf and hpf for signal separation

How much unwanted signal occurs in each output channel? That depends on the frequency separation between the signals. If the two signals are about a decade apart then the attenuation of the unwanted signal will be at most 20 dB with first-order lowpass and highpass filters.

3/ Higher-order lowpass filters, Butterworth filters

If two signals have a small frequency separation or if attenuation of the unwanted signal needs to be very large, higher-order filters are required. The pole-zero diagrams of the class of lowpass Butterworth filters of order 1-9 are shown below.

The system function for the nth-order Butterworth filter, ${H}_{n}\left(s\right)$ , is obtained from the property

${H}_{n}\left(s\right){H}_{n}\left(-s\right)=\frac{1}{1+{\left[\frac{s}{{\mathrm{j\omega }}_{c}}\right]}^{2n}}$

where ${\omega }_{c}$ is the cut-off frequency.

Each additional order of Butterworth filter adds an additional attenuation of −20 dB/decade. The frequency response for the nth-order Butterworth filter, ${H}_{n}\left(\mathrm{j\omega }\right)$ , is obtained from the property

$\left(\mid {H}_{n}\left(\mathrm{j\omega }\right)\mid {\right)}^{2}=\frac{1}{1+{\left[\frac{\omega }{{\omega }_{c}}\right]}^{2n}}$

The frequency responses are shown for n in the range 1-9 and for ${\omega }_{c}\text{=}1$ .

VII. RESONANCE AND BANDPASS FILTERS

1/ Resonant systems arise in many physical contexts

M is mass, B is a friction constant, K is a spring constant, f(t) is an external force, and v(t) is the velocity of the mass.

A second-order system function relates the velocity to the force

$H\left(s\right)=\frac{V\left(s\right)}{F\left(s\right)}=\frac{\frac{1}{M}s}{{s}^{2}+\frac{B}{M}s+\frac{K}{M}}$

Such a mechanical system yields a damped oscillation in response to a force provided the damping is not too large. For example, a tuning fork may be modeled by such a mechanical system.

2/ RLC filter

Electric networks also show a similar system function. The impedance of the RLC circuit is also of second-order

$Z\left(s\right)=\frac{V\left(s\right)}{I\left(s\right)}=\frac{1}{\text{sC}+\frac{1}{R}+\frac{1}{\text{sL}}}=\frac{\text{sL}}{{s}^{2}\text{LC}+s\frac{L}{R}+1}$

3/ Resonance parameterized

We can parameterize these and any second-order systems efficiently. We illustrate with the electrical network.

what is the stm
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research.net
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Damian
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Berger describes sociologists as concerned with
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text:
# A force acting on a particle moving in the xy plane is given by F=(2yi+x^2 j)N, where x and y are in meters.

The particle moves from the origin O to a final position with the coordinates as x=4.65m and y=4.65m, which is also represented in the following figure.

Figure 1

1. Find work done by F along OAC
2. Find work done by F along OBC
3. Find work done by F along OC
4. Is F conservative or non-conservative?

This problem aims to find the work done by the particle moving in the xy plane as it moves to the new position with the given coordinates. The concepts required for this problem are related to basic physics, which includes work done on a body and friction force.

The concept of work done comes as the dot product of the horizontal component of the force with the direction of the displacement along with the value of the displacement.

$F_s = F_x = Fcos \theta \space s$

The component that is responsible for the movement of the object is $Fcos\theta$, where $\theta$ is the angle between the force $F$ and the displacement vector $s$.

Mathematically, Work done is a scalar quantity and is expressed as:

$W = F \times s = (Fcos \theta) \times s$

Where $W=$ work, $F=$ force exerted.

Part A:

Work done by $F$ along $OAC$

We are given the following information:

Force $F = (2y i + x^2 j) N$,

The displacement in the direction of $x = 4.65 m$ and

The displacement in the direction of $y = 4.65 m$.

To calculate the work done, according to the given figure we are going to use the formula:

$W=\dfrac {1}{2} \times\ x \times y$

$W=\dfrac {1}{2} \times\ 4.65 \times 4.65$

$W=\dfrac {1}{2} \times\ 21.6225$

$W= 10.811 \space J$

Part B:

Work done by $F$ along $OBC$

Force $F = (2y i + x^2 j) N$,

The displacement in the direction of $x = 4.65 m$ and

The displacement in the direction of $y = 4.65 m$.

$W=\dfrac{1}{2} \times\ x \times y$

$W=\dfrac{1}{2} \times\ 4.65 \times 4.65$

$W=\dfrac{1}{2} \times\ 21.6225$

$W=10.811 \space J$

Part C:

Work done by $F$ along $OC$

We are given the following information:

Force $F = (2y i + x^2 j) N$,

The displacement in the direction of $x = 4.65 m$ and

The displacement in the direction of $y = 4.65 m$.

The position of particle at the point $C = (4.65 i+4.65 j)$

To calculate the work done we are going to use the formula:

$W_{particle}=F \times s = (2y i + x^2 j)(4.65 i+4.65 j)$

$W_{particle}=(2(4.65) i + (4.65)^2 j) (4.65 i+4.65 j)$

$W_{particle}=143.78\space J$

Part D:

Non-conservative Force

## Numerical Result

Part A: $10.811\space J$

Part B: $10.811\space J$

Part C: $143.78\space J$

Part D: Non-conservative Force

## Example

Find the work done in driving a cart via a distance of $50 m$ against the force of friction of $250N$. Also, comment on the kind of work done.

We are given:

The Force exerted $F=250N$

Displacement $S=50m$

$W=F\times S$

$W=250\times50$

$W=1250\space J$

Note that the work done here is negative.

Image/Mathematical drawings are created in Geogebra.