text:
# blueollie

## River City Marathon and Mike Tyson

I won’t lie: my marathon performance was dreadful.

Time: 5:44:55. Place: 303/328 overall, 172/181.
Splits (note: for some reason, mile markers were not there except for mile 10, 20, 21, 22, 23, 24, 25, 26)

1:02:02 at 5.8 (1:05:56 at 10K)
2:21:23 at 12.7 (2:25:30 at the half)
3:40:56 at 18.4 (3:44 at 30K)
4:05 at 20.
Basically: 2:25:30/3:19:25.

Excuses:

It was HOT. The course, while it featured some shade, was mostly open to the sun, and you could just feel the heat bubbling off of the pavement. Even worse: it was a sudden warming; there was little chance to get acclimatized to it.

So, FOR TODAY, finishing was good enough for me; at half way I was unsure that I would finish. At mile 18, I realized that I could walk easily (and steadily) and finish under the cut-off, and that is what I did. Note: this doesn’t mean that it was an easy effort for me; it wasn’t. But it does mean that much of my challenge in the second half of the race was to stay on “this side” of getting sick; I wanted to keep the effort to where my body could continue to digest fluids; I couldn’t afford to get into a place where the water/sport drink just sat in my stomach, doing me no good.

So, I was never aerobically taxed; it was me against the heat and that is not something that I can “work through”; I have to surrender to it.

What does any of this have to do with Mike Tyson (the boxer)? Mike Tyson famously said: “everyone has a plan until they get hit in the mouth.” Today, the heat socked me right in the kisser.

More details:
The race started downtown. I drove Mat to the race (he had a fine 25K: 2:25). His wife was to pick him up.
I chatted with many prior to the start. It was very easy to get into one’s pace; it wasn’t crowded at all.
But: I didn’t see a single mile sign until mile 10, and then not another one until mile 20; then they were there every mile. I wonder why.

I got into a “run 9, walk 1″ (minute) rhythm at the start and that seemed to be ok. Seemed. It was somewhat overcast at first and it seemed as if I were taking it easy. But one storm cloud: the 4:30 pace group was too close to me (bad) and the 4:45 pace group was behind me (not good). I should have been somewhere around the 5 hour group. I was to see (what was left of them) later…and the 5:30 too.

The first hour was uneventful though I decided that I was still working a bit too hard so I switched to a 4-1 rhythm, though I allowed myself to walk up the first good uphill that took you out of town. I felt (ha ha) that I was in the place I was to finish.

Then came many of the roads that I was familiar with, including Bradley university, my neighborhood (we passed right in front of my house!) and my 5 mile West Peoria “lunch” course. I got encouragement from many who are used to seeing me run in the neighborhood. That was nice. Barbara yelled encouragement before leaving to work the 25 mile water stop.

Along the way, I saw Tracy (mile 13.5), Larry (mile 13.75), and Herb (mile 14.5 or so). I was about 2:30 when I saw Tracy, and I told her that I would probably need at least 3 more hours to finish; she told me (as did others) that I “looked good”.

I wasn’t athletically distressed in terms of expending effort going fast. But I was feeling the heat and getting that “if you get hotter, you won’t be able to process fluid anymore” feeling. I’ve had that before: the liquid just sits in your stomach and does nothing but make you sick.
So, I had my right foot (sole, under the ball of the foot) whining (a frequent “hot spot” for me) so I took a Tylenol …and sure enough, the pain went away. That meant that I was digesting liquid; a good sign.

During this stretch I started to do “3-2″ (run 3, walk 2) and even that was challenging. I took a few “just walk all 5 minutes” segments.

At this time, the 25K cut away from our course and back; at the intersection of Sheridan and Main, the real “forever” split came: 25K runners ran downhill to the finish; marathon runners turned left for a LONG 10 more miles.

At this point, Melody passed me (and was to beat me by more than 30 minutes).

I decided to stick it out.

Up through the neighborhoods: I got to mile 18 and, while not athletically defeated, I was on the ropes, heat wise. Ice from aid stations were a life saver. I could still drink though and that was the key…but I could feel the point of “no longer able to digest” coming so I made the decision to walk the rest of the way (save one good downhill that was made for jogging). I was at about 3:35 into it and figured I should be able to walk 16-16:30 mpm without endangering my ability to digest liquid….and that would get me the finish.

And that is what I did.

I still got passed a lot though, and Rich Breaux passed me at about mile 22 with a crack “the best laid plans of Mice and Men” (and marathon runners?) I laughed and wished him well; I told him that I wanted the sub 6 hour finish and he reassured me that I could walk it in.

Hey, I got to see the rest of the crowd though, as well as to enjoy the shady neighborhood in the finishing stretch. I saw Barbara at the aid station and she knew that I was behind schedule. But I told her that “today, a finish is good enough.”

And it was…I was even able to bring Froggy out and wave her around as I crossed the finish line.

I got a LOT of encouragement from others: Terri Brink, Herb, Larry, Tracy, Jennifer, Barbara and from many others. And it really, really helped. It encouraged me to stick it out, even at a suboptimal performance (to say the least!).

Afterward, I got to talk to T and her husband Fred…and maybe obtain a football watching buddy for the Illinois games this season?

What I learned I got a good sense of when I am about to “cross the line” into the “no longer able to digest stuff” zone; once I am there, it takes HOURS to get out of it. This knowledge might serve me well for future 12-24 hour races.

And I’ve come to grips with the following facts:
1. I SUCK when it is hot.
2. Making gains on one’s bench press and pull ups is NOT good marathon training.

Barbara is yelling “get going Lard Butt” at me…and probably checking out that guy.

May 19, 2013

## Kudos to my Sister, a young man and the Riverplex staff…and my wife.

Workout notes: part II
I warmed up on a warm day: I jogged a 10 minute mile to the Marina and then ran an 8:30 mile back. The second mile was harder than the first.
Then 3 miles with the group; Stacey (my main trainee) is improving each week.

However, my fanny pack (great for walking and hiking) became unzipped; I forgot how much running jars it.

Evidently my cell phone fell out.

So, while my wife called to get the service suspended, my Sister e-mailed me. Evidently, the person who found the phone called the name marked “Mom”.

So I got the e-mail which sent me to the Riverplex where a smiling staff member had it waiting…while my wife turned the service back on.

All of this because of my f**k-up.

So the next time you hear me complaining about going extra because of someone else’s screw up, feel free to remind me of this.

And…if you use your fanny pack (the one that you use to walk and hike): if you run, be sure the zippers (both of them) are all the way down at the side, else the pack unzip itself.

May 16, 2013

## Fun Fun Fun and Weights…

Workout notes
Very leisurely weight workout:
Supplemental stuff: rotator cuff, hip hikes, Achilles, side plank, light squats (5 x 50, 5 x 75)
The squats were more for stretching than for strength. The goal is to be able to build up to doing real weights.

Meat:
pull ups: 15, 10, 10, 10, 10
bench: 10 x 135, 4 x 185, 7 x 170
dumbbell military: 3 sets of 12 x 50 (seated, supported)
dumbbell rows: 3 sets of 10 x 65 (each arm)
dumbbell bench: 2 sets of 10 x 65
ab sets: 3 sets of 10 of crunch, twist, sit back, vertical crunch (curl that torso!)
incline press: 10 x 140, 8 x 140
pull downs: 3 sets of 10 x 160
pulley curls: 3 sets of 10 x 57.5

No, I didn’t do this exercise nor did I see her:

Stuff I am signed up to do tomorrow’s Race For the Cure. I’ll have to be careful to not line up too far back as this year, the men and women start together (that is unfortunate). I will of miss running through the wave of 12-13 minute milers at about mile 2 and the 11 minute milers toward the end, as I am doing here in the 2009 race. My time was a mid 24.

Fun I have a fast racewalking friend; her WALKING marathon PR (4:19) is sure to be faster than the one I am scheduled to run in a week. She posted some video of her training. She told me that I’d like it. She made a longer video for her coach to critique. I took the liberty of taking a small portion of it.

May 10, 2013

## Ames Iowa, Day II (lunch)

Workout notes
I didn’t sleep well (Mexican meal too heavy last night?)

I got up early and walked 4.47 miles in 1:06 (14:52 pace) doing roughly the same course I did yesterday, minus a .7 mile out and back and a .3 out and back near the soccer fields.

It was in the 40′s and crisp; I got to see the sun rise.

Talks: the morning talks were good but tough; still I managed to pick up techniques at every one of them.
Several people said that they would have to leave prior to my talk; I expected that (4 pm slot). Some might still be there and I owe them a professional effort; I practiced my talk twice.

Campus: very pretty

April 28, 2013

## Should you run or walk? It depends….

If you’re a runner, you might have noticed this surprising headline from the April 5 edition of the Guardian: “Brisk walk healthier than running—scientists.” Or maybe you saw this one, which ran in Health magazine the very same day: “Want to lose weight? Then run, don’t walk: Study.”
Dueling research from rival academic camps? Not exactly. Both articles described the work of a herpetologist-turned-statistician at the Lawrence Berkeley National Laboratory named Paul T. Williams, who, this month, achieved a feat that’s exceedingly rare in mainstream science: He used exactly the same dataset to publish two opposing findings.
One of Williams’ papers, from the April issue of Medicine & Science in Sports & Exercise shows that habitual runners gain less weight than habitual walkers, when the amount of energy they put into their exercise routines is the same. The other, published in April in Arteriosclerosis, Thrombosis, and Vascular Biology, used a similar analysis to show that running is no better than walking when it comes to the prevention of high blood pressure, high cholesterol, diabetes, and coronary heart disease. So there you have it, and there you don’t. Running is better for your health, or perhaps it isn’t.

The Daniel Engber article continues on and I recommend reading it.

Of course, these aren’t contradictory findings; weight loss and those other factors, while linked, aren’t exactly the same.
And, of course, the premise is that you are doing this activity mostly for health reasons.

I’ll weigh in with my story: These photos are from 2009. The first shows me walking the Quad Cities Marathon in 5:28 (walking the whole way; it turns out that I was walking with a meniscus tear in my right knee but didn’t know it at the time). The second shows me running the Race for the Cure 5K in 24:29; that was a typical 5K running time for me that year. Note: if seeing me around walk/runners in the second photo confuses you, in this race, the women were given a 10 minute head start. Hence I was weaving around the slower walk/runners and faster walkers when this photo was taken.

I’ve walked in races from 1500 meters (fully judged racewalk) to 24 hours and have walked (no walking judges) races from local 5Ks to 24 hours and 100 miles. Best times: 4:44 marathon powerwalk, 6:20 50K powerwalk, 11:13 50 mile powerwalk, 101 miles in 24 hours, 2:17 half marathon, 30:42 5K (judged), 18:03 3K (judged), 8:31 1500 (judged).

I’ve run quite a few races too; best times: mile 5:30 (1980), 5:41 (1600 meter 1998), 5K 18:57 (1982), 19:53 (1998), 10K: 39:50 (1982), 41:27 (1998), half marathon 1:34, (1999), marathon 3:33 (1980), 3:38 (2000), 3:40 (2001).

Currently: running: 24:33 5K (2012)…25:00-25:30 is typical, 1:22:46 15K (2013), 2:01 half marathon (2013)
I haven’t had a good walking marathon in a while (did a 7 hour walking marathon in 2012 when I got sick and had to rest for 1 hour at an aid station), but my half marathons in 2012 were 2:34, 2:30 and 2:25. I did 2:22 in 2011. Also, in 2011, I walked 54 miles in a 24 hour event. Note: I can’t legally racewalk any more as my right knee no longer straightens all of the way.

Running or walking? Here are the differences, as I see them:

1. Running: I sweat more. I get wetter and in cool weather, my glasses fog. Not so much when running.
2. Injury wise: running is harder on the feet, knees and Achilles tendon. Walking is harder on the piriformis (small but muscle), hips and hamstrings.
3. Recovery: I definitely recover from walking races quicker than I recover from running races. For a period (prior to getting a piriformis injury in 2006), I could do lots of marathons with no ill effects; in fact in 2009, I managed to get 2 marathons, a trail 30 miler, a trail 100 miler and 66 miles in 24 hours all in the same year. That was my last “active” year for long distances.
4. For me, the calorie requirement is higher for running than walking, and an easy run requires more exertion than an easy walk.

So, what to do? Right now I am running more than walking but that ratio might change soon as my piriformis appears to be feeling better. So, ideally, I like to run distances from 2 miles to the half marathon, and walk distances from the half marathon to the 50K.

In terms of working out, I enjoy the 6 mile (10K) to 10 mile (16 km) distances the best; it is enough to be distance but short enough were I can push the pace a litte. Walking: I enjoy 10 mile (16 km) to 15 mile (25 km) the best; these are longer workouts than the run but somewhat gentler.
Note: I also enjoy hiking from time to time; I like hikes of 6 miles (10K) to 10 miles (16 km) the best.

But my natural gait is sort of “walk-ish”; others have trouble figuring out whether I am trying to walk or trying to run (others usually think that I am walking all of the time).

As far as what is the best for you: I’ve enjoyed mixing the two up (run one day, walk the next, or follow a run with a walk). I’d say: “be honest with yourself”. If you are new to sports and are trying to run…and you look as if you are doing the foot dragging shuffle: I recommend learning to walk fast. Walking allows for you to put your bigger gluteal muscles into it and the propulsion is with a push-off…and you don’t have that “flight phase” in which BOTH feet are off of the ground at the same time.

But if you have a sports background and your body can tolerate running…AND if you enjoy it, then hey, run.

What you should do: whatever you will stick with. If you hate it, you won’t stay with it. If you frequently injure yourself, you won’t stay with it.

Don’t worry about which is optimal.

## Bradley Women Soccer 5K plus …

You see the course profile. Just the facts:
8:20, 8:14, 8:05, 0:49 25:29 for 5K
2 miles warm up plus 2 miles cool down = 7 miles total

This was a tiny race; 20-30 tops. Early on a young woman was leading and I was chasing 2 young women, an older guy and a young man. I caught none of them.

The course started with a right hand turn and then an up/down on the toughest hill on the course. We came down and on the downhill I passed the two women and the old guy; they got me back on the next uphill. Then it was pretty much the same on the rest of the course though they eventually picked up the pace.

The day was pretty and I ran hard; this was just a challenging 5K.

Next I ate some breakfast and then went to the East Peoria bikepath to walk 8 more miles. I kind of lolly-gagged going up (1:01 to 4.05) and then, inspired by some slower women runners (that I couldn’t catch) took the return in 55 minutes; 40 for the last 3. That was a better effort.

Why? I’ll be walking much of the marathon so I need to practice walking.

## No Respect….

Workout notes Great weather; walked my Cornstalk classic course in about 58 minutes (by time of day; I had to wait to cross streets, etc.) This was about 13:30 mpm or so on a hilly course; it was just hard enough to get slightly damp with sweat.

I am feeling better, but this mini-workout took something (just a little) out of me. There is no way in Hades I could have done this 7 times in a row (enough to make 30 miles) today. And yes, I’ve walked 50 miles in a row at a faster pace…a LONG time ago.

Later, my wife tells me that one of her former students (in his early 30′s) ran his first half marathon in 1:54. “That’s good, right?” she asks. I reminded her that when I was 39 and 40, I had run a 1:42 (windy; a month after a marathon) and a 1:35 (peaked) and she had yelled “get going Lard-Butt!” at me as I finished (25-30 minutes behind the winner). So, is he (her former student) a lard-butt? “No…that’s different.”

No respect.

Social
I got this e-mail message from Rick Santorum:

Grab the popcorn folks; this will be fun.

Awesomeness

See the earth through Saturn’s rings…and Saturn, with rings, from the earth via the moon:

The view from the other direction:

April 7, 2013

## Hiking, Science, Math and funny videos…

Workout notes Slow, easy hike (1:09 outer loop, 54 minute out and back for 2:03 for 10K) at the hilly Forest Park Nature Center. There were several other hikers out there. One middle aged lady was struggling with a hill; she said that she “bit off more than she could chew” with her first hike of the season. We agreed that if there is a time to get stiff and sore, it is now.

It was a very pretty day; the best we’ve had in a while.

Observations: the vast majority of hikers are slender; today I saw a couple of exceptions.
The parking lot: what struck me is that there were several hybrid cars and no large trucks; there were a couple of smaller SUVs. This is very different that what you see in the parking lot of the all-you-can-eat restaurants.

Humor and working out:

Video
Why would ANYONE think of me when they saw this on Curb Your Enthusiasm?

Science
Here is an article about these “caveman diets” and the fallacy of “if it is natural it must be better” medicine/diet. Note: I know that some people simply can’t eat certain foods (e. g. my wife has celiac disease, which was diagnosed by a blood test given by a doctor.)

Mathematics

Now I think that I know what is meant by this: if someone says “x is obvious and therefore does not require proof” they are on dangerous ground. Though there are a few all-time-great mathematicians that can make correct conjectures that aren’t proven until much later, the vast majority of us had better be able to prove what we claim; our intuitions, while necessary and valuable, can lead us astray.

For example, I once spent 2 years trying to prove something but couldn’t; the reason: it was false! Happily I eventually sought out and found a counterexample and published that.

You see some “obvious facts” (which are false) repeated over and over again!
For example, in some quantum mechanics text books and notes, you see the claim: if $\int^{\infty}_{-\infty} \psi^2(x) dx$ is finite and exists then $lim_{x \rightarrow \infty} \psi(x) = 0$ which is FALSE, even if $\psi$ is smooth.

Note: if you don’t know this, and want some hints:
1. Think: convergent infinite series
2. Think: a sequence of tall, thin rectangles that get taller and thinner; each area is the value of the term of your favorite convergent infinite series.
3. Smooth with a bump function.

Of course, the uninitiated are sometimes confused by this saying and said this (on someone else’s wall):

“Yeah, cause we wouldn’t want any part of mathematics to be intuitive or anything human-like.”

I don’t know the spirit with which this was said. But this LOOKS (to me; but I could be wrong) like “if it is too opaque for me to understand it must be bad”. You do see attitudes like this a LOT.

But the blunt truth: mathematics, science and engineering are hard, and progress at both the theoretical and practical levels is difficult. Smart people have to work hard and put forth a great deal of intellectual effort. But the results: well, efficient engines, medicines, modern electronics, this computer, etc. “Common sense” is woefully insufficient at the research levels, even if it is necessary to be successful in one’s day to day life and one suffers if one lacks it.

March 31, 2013

## A case study of non-critical acceptance….

Workout notes: yes, the piriformis is moderately achy, but I walked two easy miles and did some PT, yoga, exercise ball stuff, etc. It should be feeling ok by the end of the week.

Posts

See the flaw here? If you don’t ask yourself:
1. Did Ronald Reagan collect more revenue than, say, Teddy Roosevelt? (yes, he did).
2. What happens to revenue collections when incomes go up? Remember that the proponents of supply side economics often repeat the mantra “low tax rates leads to high tax revenues”.

Of course, this is aimed at conservatives that absolutely despise President Obama, and so few ill ask if this makes any sense at all. And, yes, some won’t see why this is a bogus argument, even when it is explained to them…and many of these people see themselves as “smart”. Yes, this phenomenon is not one sided; liberals do it too.

Now for this phenomenon applied to science:

this is a viral video and I admit that the graphics are cool. But:

Well, one (correct) take away from this is that while we have a (sort of) two dimensional solar system model with the sun as the reference point, one can also take a galatic point of view to see that the sun traces out an orbit in the galaxy; therefore the planets do too. For that matter, one can take a universal look and see our galaxy (and hence our solar system) expanding within our spatial universe, but never mind that.

There are some problems with this video. For one: “vortex” isn’t the right word; the video author means that, if one uses a center of the galaxy as a reference point, then the trajectory traced by the planets is a (sort of) helix. The other thing: the planets don’t “drag after” the sun as it moves; in fact the angle of inclination of the “orbit planes” (they are slightly different) is about 60 degrees with respect to the sun’s trajectory around the galaxy and not 90 degrees; hence at times the various planets actually “lead” the sun. There are other problems as well; here is a very nice summary.

Just because something looks cool doesn’t mean that it is reality.

Back to Politics
This is expensive stupidity for the sake of helping people feel better:

To fight the specter of poor people spending taxpayer money on drugs, a Republican congressman has reintroduced legislation to make welfare applicants pee in cups to prove they’re clean.

Rep. Stephen Fincher’s (R-Tenn.) bill would require states to randomly test 20 percent of people receiving benefits from the Temporary Assistance for Needy Families program, which spends roughly $16 billion per year supporting poverty-stricken parents with monthly checks averaging$392.

“Currently the federal government enables drug abusers a safety-net by allowing them to participate in the TANF program,” Fincher said in a statement. “Instead of having to make the hard-choice between drugs and other essential needs, abusers are able to rely on their monthly check to help them pay their bills.”

In Congress and in state legislatures across the country, Republicans have sought to implement welfare drug testing programs in recent years. Few measures have become law, as testing can be expensive and there’s not much data reflecting a widespread drug problem among welfare recipients. Civil liberties advocates successfully sued to halt the most sweeping drug screening law, implemented in Florida in 2011.

In fact, here is what happened in Florida:

Florida’s four-month drug-testing run in 2011 yielded 108 negative drug tests, according to Department of Children and Families data. Only 2.6 percent of applicants who took the test failed, though supporters of the law say that does not account for people who walked away from the application process because they were on drugs.

The pass rate was 96.3 percent, leaving the state to pay more than $100,000 to adults who paid for the test and passed. The average time an adult receives TANF is four and a half months, said DCF spokesman Joe Follick. In short, you are paying a lot of money to screen out a few slackers (those who failed, and those who walked away). This makes no fiscal sense, but it is politically popular because “everyone is against druggies getting welfare”. No money was saved: From July through October in Florida — the four months when testing took place before Judge Scriven’s order — 2.6 percent of the state’s cash assistance applicants failed the drug test, or 108 of 4,086, according to the figures from the state obtained by the group. The most common reason was marijuana use. An additional 40 people canceled the tests without taking them. Because the Florida law requires that applicants who pass the test be reimbursed for the cost, an average of$30, the cost to the state was $118,140. This is more than would have been paid out in benefits to the people who failed the test, Mr. Newton said. As a result, the testing cost the government an extra$45,780, he said.

And it is the Republicans that have all that good “business sense”??

By the way, when I was in the Navy, I was subject to drug testing. But I served on a nuclear submarine; the consequences of someone serving while “high” (which did happen) were potentially catastrophic; it was a serious safety issue in that case.

March 4, 2013

## Whack a Mole with Terrorists…

Workout notes 5K treadmill walk after weights.
Treadmill: I started out at 4.1 miles per hour (about 14:40 mpm) and upped the incline by 1 every minute until I got to 7 at 14 minutes; then I kept it there until 30 minutes. Then I lowered the incline by 1 unit every 2 minutes up upped the pace by .1 mph until I was a 4.8. total time: 42:20 for 3.1 miles.

Weights: rotator cuff, pull ups (4 sets of 10, 1 broken set of 10), incline: 10 x 135, 4 x 155, 6 x 145, 8 x 140.
rows/dumbbell bench: 3 sets of 10 x 65 lb. dumbbells. seated dumbbell military: 2 sets of 10 x 50, 1 set of 15 x 45. Pulldowns: 3 sets of 10 x 160. Curls: dumbbells (10 x 70), machine (10 x 70), EZ curl bar 10 x 55. I also did the ab line 3 times (10 x weighted crunches, twists, sit backs, vertical crunches) and legs 3 times (adduction, abduction, push backs) and some stretches.

I felt good.

Not so good
How bad is it in Pakistan? There is a terrorist group there whose mission is simply to kill Shia Muslims:

The group doing the killing is called Lashkar e Jhangvi, “The Army of Jhangvi” or LEJ. They are Sunnis whose agenda is not much more nuanced than killing Shias. Though South Asia is a region rife with internecine conflict, with factions who have fought each other for all of recent history over land and religion, these attacks are unique. Even in a region violence visits far too often, what’s happening now is singular, and it’s getting worse.

First it was snipers picking off civilians, then LEJ members began stopping busses, shooting Shia passengers and leaving their bodies on the roadsides. Now, LEJ is using massive bombs in places frequented by Shia civilians: social clubs, computer cafes, markets and schools. About 1,300 people have been killed in these attacks since 1999, according to a website dedicated to raising awareness about them. More than 200 have been killed so far this year.

Hazaras are one kind of Shia for which LEJ has a particular fascination. Quetta sits just below the border with Afghanistan, and it’s the city where members of a Shia group from Afghanistan–the Hazaras–have sought refuge whenever they’ve felt their own country doesn’t want them. They’ve been coming to Quetta for over a hundred years, but while they’re coming in search of safety, they’re now being met with slaughter. [...]

If the Taliban is the schoolyard bully who keeps some semblance of order among the other children but then begins to abuse his power, LEJ is the hyperactive kid running around kicking shins, and who has free reign because the teachers are terrified of him, too. After a bombing last month, LEJ waited until rescue crews arrived at the scene, and then set off a bomb to kill them, as well. The message was clear: If you try to help Hazaras, you will end up like them.

Fear may explain why the government isn’t doing anything about the attacks. LEJ is not hard to find and their leadership lives openly, mostly in Punjab. They do not pursue their means discreetly. The bomb LEJ used in February weighed 2,200 pounds, twice the size of the one Ramzi Yousef used to try to topple the World Trade Center towers in 1993. They had to tow it to the bombsite behind a tractor.

Nor do the killers try to avoid blame. On the contrary, they eagerly accept responsibility, post YouTube videos of themselves and tally up death tolls with transparent glee. A twitter update just after a recent attack read:

“Quetta Alert: 50 Shias in hell and over 65 injured due to blast on Alamdar Road.”

If anyone thinks that there is some moral equivalence between the United States and groups like this, they are crazy.

February 27, 2013


text:
# Making data visualisations in RStudio

This article will guide you through isualization with ggplot2 u- Setting Data, Aesthetics and Geometries

Making data visualisations in RStudio.

## Data Visualisation with ggplot2

Introduction

Let’s load our data set of interest, install and load all the packages we need, and start making data visualizations in RStudio.

Good practice

A good practice is to load the packages you need before starting your analysis. It is also recommended to write the packages you need in the script you prepare for a project. This is a list of convenient packages to use with ggplot2

> library(ggplot2)
> library(RColorBrewer)
> install.packages("viridis")
> library(viridis)

Note. Another widely used package in data science is called tidyverse, and is a collection of packages including ggplot2, dplyr and many other helpful resources. It can be worth trying to use it on your own after this course.

## Setting your working directory in RStudio

Step 1. We recommend you to work in the Project folder Project_Test that we created previously, either by clicking directly on the Project_Test or using the following command

> setwd("/Users/imac/Desktop/exerciseR/Project_Test")
> getwd()
[1] "/Users/imac/Desktop/exerciseR/Project_Test"

Step 2. As a reminder, you can create a specific script file to write your commands and related comments.

Step 1. Import or load the iris dataset we want you to work on in RStudio. All options are identically accessed in R, but the two final options are particular to RStudio.

• From your computer, if you placed the iris dataset file in your working directory

> Iris <- read.table("iris.txt")

• From your computer, if the iris dataset file is in the parent folder exerciseR

> Iris <- read.table("/Users/imac/Desktop/exerciseR/iris.txt")

• From the available data sets in R

> data(iris)

• From the “Import Dataset” tab in the Environment, by selecting the correct file with its type and parent folder.

• From the File menu, by choosing the “Import Dataset” option.

Note 1. Be careful to choose the “iris” dataset as “Iris” would here correspond to the same data set but with changes that could impede the rest of the commands.

Note 2. As other functions in R, the “read.table()” function has different options that you can view in the following link, which also shows you other functions used to import data from other file formats (for example with the “read.csv()” function to read “.csv” files). https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/read.table.

Step 2. You can also display and work on specific data chosen from the iris data set

> iris_length <- iris %>% select(Sepal.Length, Petal.Length)
Sepal.Length Petal.Length
1 5.1 1.4
2 4.9 1.4
3 4.7 1.3
4 4.6 1.5
5 5.0 1.4
6 5.4 1.7

## Setting Aesthetics and Geometries

Step 1. Let’s use basic layers to plot Petal.Length vs. Sepal.Length. With ggplot2, “aes()” specifies aesthetics for x and y-axis, and “geom_point()” generates a scatterplot

> ggplot(data = iris,aes(x = Sepal.Length, y = Petal.Length)) +
geom_point()

Note 1. Here is an example of how you should see the output in your “Plots” area in RStudio. Note that you have the possibility to save your plot using the “Export” button, with options related to file formats. Other R options we saw for saving plots remain possible.

Note 2. We will not show the whole area again, but remember that the plots you generate will appear here.

Step 2. Using the same previous plot options, let’s color the points according to the Species

> ggplot(data = iris, aes(x = Sepal.Length, y = Petal.Length, color = Species)) + geom_point()

Step 3. There are other possible shorter ways for generating this same output

> ggplot(iris, aes(Sepal.Length, Petal.Length, color = Species)) +
geom_point()

Note. However, for the sake of clarity, we will mainly keep the full details such when using data, x and y to ease the understanding

Step 4. It is possible to create a variable with your base aesthetics and then simply call it to apply other layers. The following will create the same output as the previous graph

> key <- ggplot(data = iris, aes(x = Sepal.Length, y = Petal.Length, ,
color = Species))
> key + geom_point()

Step 5. Different geometries can also be used to complement each other. Here “geom_smooth()” adds a trend line and area to the points

> key + geom_point() + geom_smooth()

Step 6. You should have noticed how geometries are here added with default options. Each has a set of options, such as removing the trend area in the following with se=FALSE

> key + geom_point() + geom_smooth(se=FALSE)

Step 7. You can easily change the points size, shape and colour from “geom_point()” options, but see how it affects the display: if you force one colour, you will not have any more colors by Species, even if they are required in the key variable

> key + geom_point(size=4, shape=15, color="red3")

Step 8. Or the size, shape and color as dependent now on Sepal.Length values from aes

> ggplot(data = iris, aes(x = Sepal.Length, y = Petal.Length,
color = Sepal.Length, size = Sepal.Length)) + geom_point()

Note. We used here the default ggplot2 colors, but we will see later on how to use other color palettes

## Other Functions and Plots

Step 1. Remember that we are only covering here the “ggplot()” usage, but other possibilities exist to generate the same output as in Step 6 of this Article, such as “qplot()” which is used to generate quick plots with ggplot2

> qplot(Sepal.Length, Petal.Length, data = iris, color =
factor(Species)) +
geom_point() +
geom_smooth(se=FALSE)

Step 2. Generating different plots will require different geometries

• Boxplot with default options

> ggplot(data = iris, aes(x = Sepal.Length, y = Petal.Length,
color = Species)) + geom_boxplot()

• Bar plot with default options

> ggplot(data=Iris,aes(x=Sepal.Length)) + geom_bar()

• Or more complex ones even with default options such as Density plot

> ggplot(data=Iris,aes(x=Sepal.Length, y = Petal.Length)) +
geom_density_2d_filled()

Step 3. An important thing to remember is that each plotting functions comes with its own set of option, that might not work for other functions. Let’s see how to generate and modify histograms

• Default options

> ggplot(data=Iris,aes(x=Sepal.Length)) + geom_histogram()

• Filling histogram colurs by Species. Note how calling the colour option is different here

> ggplot(data=Iris, aes(x=Sepal.Length,fill=Species)) +
geom_histogram()

• Use binwidth option with histograms

> ggplot(data=Iris,aes(x=Sepal.Length,fill=Species)) +
geom_histogram(binwidth = 0.05)

Note. A wide range of different plots can be generated with ggplot2 such as Bar plots, Boxplots, Violin Plots, Density Plots, Area Charts, Correlograms…and many many more !

format: plain


text:
# Matrix product (notation in answer)

Suppose I have a matrix $C=\begin{bmatrix} 1 & 0 \end{bmatrix}$ and a vector $\mathbf{x}=\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$.

I want to write the matrix product $C\mathbf{x}$, should the answer be vector notation (bold) or not?

I mean vector notation $$\mathbf{y}= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1$$ or scalar notation $$y= C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=x_1$$ I use upright letters for matrices, bold letters for vectors. Non-bold for scalars.

$$C\mathbf{x}=\begin{bmatrix}1 & 0\end{bmatrix}\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}=[x_1]$$ (note the brackets around $x_{1}$) is a
• $1 \times 1$ matrix, or
• Thanks! But using scalar notation $y$ (not bold) is wrong? – JDoeDoe Dec 21 '16 at 11:48


text:
## [DM15L] Got mine

This is the place to discuss the usage of DM1x/DM41 machines and to share any tips & tricks you may have stumbled across.

If discussing a specific model, please ensure that you prefix topic subjects with the model number this way:

[DM41] How to change the number of program steps available
Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### [DM15L] Got mine

First: looks great, fast delivery.

Then:
• Only one rubber foot holding a little grip (upper right)
• Some sort of dirt under the display (2nd digit from the right). It's not a dot matrix thing, bec. when I press on the glass it doesn't vanish like other LCD cells.
• How do I kill f- or g-keystrokes. Supposed I want e^x but I pressed 'g' for ln, all I can do is switching the calculator off.
• When I want to circle through the fonts, after 7 ON I must switch the calc off, then again 7 ON. With just 3 fonts it's no mess (don't have a quadzillion fonts like Windows) but nevertheless no so elegant. Keeping the calc in font-mode while holding the 7 pressed and circling around with ON would be better.
What disturbs me most is that the calc glides on the screwheads over my sleek office table without grip. If the screwheads wouldn't protrude or the rubbers would be higher, it would be better. Right now its screws are gliding over possibly delicate surfaces. I can circle it over a desktop around the upper left corner.
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5

Michael
Posts: 240
Joined: Wed Apr 05, 2017 11:31 pm

### Re: [DM15L] Got mine

Unfortunately the rubber feet are a bit too thin in the latest batch, or the screw heads are too large.
I should get both smaller screws and thicker rubber feet next week. Please contact me for replacements then.

Another issue is some LCD making small spots. This is a defect of the last batch of LCDs. I got a new batch which shouldn't have that anymore and advised to dispose the remaining LCD from the previous batch. Unfortunately they did not follow this order and mixed the old ones with the new batch
The good news is, fixing it is rather easy:
Put the calculator in a hot place, up to 70°C for an hour or two and the spots will be gone.
Even putting it in the car on a hot day for some hours does it, otherwise you can put it in the oven if the temperature is kept low enough.
Best would be to only bake the PCB without the housing and without the battery.

AFAIK, there is no way to kill the f and g annunciator once activated without executing a function or turning off the calculator.

Currently there no other option to cycle through the fonts.

rprosperi
Posts: 884
Joined: Mon Apr 24, 2017 7:48 pm
Location: New York

### Re: [DM15L] Got mine

You can use [f] [CLEAR PREFIX] to 'cancel' either [f] or [g] prefix keys.

If you've pressed [f], just continue with [CLEAR PREFIX].

If you've pressed [g], you must press [f] [CLEAR PREFIX].

This is the same key sequence to display the full mantissa, but it also serves to cancel the shift since it does not change stack or anything else.
--bob p

DM42: β00071 & 00282, DM41X: β00071, DM10L: 071/100

Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### Re: [DM15L] Got mine

rprosperi wrote:
Wed Jan 10, 2018 4:52 pm
You can use [f] [CLEAR PREFIX] to 'cancel' either [f] or [g] prefix keys.

If you've pressed [f], just continue with [CLEAR PREFIX].

If you've pressed [g], you must press [f] [CLEAR PREFIX].

This is the same key sequence to display the full mantissa, but it also serves to cancel the shift since it does not change stack or anything else.
Thanks! That helped a lot.
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5

Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### Played a little

First idea: to less functions on my new toy. How about a cubic root function?
I decided for branching to functions I programmed.
All under Label E, function call for cubic root is '0'

LBL E
0 ; 10 possible functions, starting with '0'. Has to be set manualy for every new function
TEST 8 ; prevents error 4 with undefinded labels
RTN ; yes? kiss and goodbye, back to sender!
R_down ; rolling down function number
STO I ; and storing it into index register
R_down ; rolling down value to be processed
GTO I ; and jumping to chosen function
LBL 0 ; here's where the fun begins
3
1/x
y^x ; calculating cubic root
RTN ; and here we are

I'd love to use the dot-labels, but I cant't address them with die I-register.

So when I want to know the cubic root of 1.000 ( ... ), I enter
1000 ENTER 0 f E
While manualy I must enter
1000 ENTER 3 1/x y^x
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5

grsbanks
Posts: 975
Joined: Tue Apr 25, 2017 11:23 am
Location: Preston, Lancs, UK
Contact:

### Re: Played a little

Krauts In Space wrote:
Thu Jan 11, 2018 6:19 pm
I'd love to use the dot-labels, but I cant't address them with die I-register.
Yes you can.

Code: Select all

12
STO I
GTO I
is the equivalent of:

Code: Select all

GTO .2
Simply add 10 to the value in the index register.
There are only 10 kinds of people in the world: those who understand binary and those who do not.

Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### Re: Played a little

grsbanks wrote:
Fri Jan 12, 2018 9:24 am
Krauts In Space wrote:
Thu Jan 11, 2018 6:19 pm
I'd love to use the dot-labels, but I cant't address them with die I-register.
Yes you can.

Code: Select all

12
STO I
GTO I
is the equivalent of:

Code: Select all

GTO .2
Simply add 10 to the value in the index register.
According to the HP15C manual to me 10 to 14 is for labels A to E.
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5

dlachieze
Posts: 220
Joined: Thu May 04, 2017 12:20 pm
Location: France

### Re: Played a little

Krauts In Space wrote:
Fri Jan 12, 2018 11:02 am
According to the HP15C manual to me 10 to 14 is for labels A to E.
As far as I can see in the HP 15C manual page 107 & 108, the Indirect Addressing table shows that I-register values:
• 0 to 9 are for labels 0 to 9
• 10 to 19 are for labels .0 to .9
• 20 to 24 are for labels A to E
DM42: 00425 - DM41X: β00066

Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### Re: Played a little

dlachieze wrote:
Fri Jan 12, 2018 11:27 am
Krauts In Space wrote:
Fri Jan 12, 2018 11:02 am
According to the HP15C manual to me 10 to 14 is for labels A to E.
As far as I can see in the HP 15C manual page 107 & 108, the Indirect Addressing table shows that I-register values:
• 0 to 9 are for labels 0 to 9
• 10 to 19 are for labels .0 to .9
• 20 to 24 are for labels A to E
In the quick reference, linked on the Swissmicros website, it's written on page 5
GTO I: I>=0: 0...9 -> LBL 0 ... LBL 9, 10 ... 14 -> LBL A ... LBL E.
I'll give it a try this weekend. I'd love that.
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5

Krauts In Space
Posts: 85
Joined: Wed Jan 03, 2018 3:48 pm
Location: Nuremberg, Germany

### Re: [DM15L] Got mine

Michael wrote:
Wed Jan 10, 2018 3:19 pm
Unfortunately the rubber feet are a bit too thin in the latest batch, or the screw heads are too large.
I should get both smaller screws and thicker rubber feet next week. Please contact me for replacements then.

Another issue is some LCD making small spots. This is a defect of the last batch of LCDs. I got a new batch which shouldn't have that anymore and advised to dispose the remaining LCD from the previous batch. Unfortunately they did not follow this order and mixed the old ones with the new batch
The good news is, fixing it is rather easy:
Put the calculator in a hot place, up to 70°C for an hour or two and the spots will be gone.
Even putting it in the car on a hot day for some hours does it, otherwise you can put it in the oven if the temperature is kept low enough.
Best would be to only bake the PCB without the housing and without the battery.

AFAIK, there is no way to kill the f and g annunciator once activated without executing a function or turning off the calculator.

Currently there no other option to cycle through the fonts.
Hello Michael!
What about the foam pads, glued to the PCB? Up to 70°C might make them shrink an vanish away Or should I not mind about them?

Annunciators: I did as rprosperi recommended but it's still a pain in the ass. Pressing the f or g key succesively should disable the annunciator.

I also would like to have that 'nulling' of a keypress like at the HP41, when a key is held down for a second.
DM15L S/# 10584 FW v25
DM42 S/# 01015 FW v3.5


text:
# How to solve this using the Chinese Remainder Theorem?

Question 1: Given the system\begin{align*} & x\equiv 3\mod 4\tag{1}\\ & x\equiv 2\mod 5\tag{2}\\ & x\equiv 5\mod 11\tag{3}\end{align*} Solve for $x$ using the Chinese Remainder Theorem.

I was taught that the remainder theorem says that given\begin{align*} & x\equiv b_1\mod n_2\tag4\\ & x\equiv b_2\mod n_2\tag5\\ & \cdots\cdots\cdots\cdots\cdots\cdot\tag6\\ & x\equiv b_r\mod n_r\tag7\end{align*} Then $x\equiv b_1c_1\dfrac {N}{n_1}+b_2 c_2\dfrac {N}{n_2}+\cdots+b_rc_r\dfrac {N}{n_r}\mod N$ where $N=\prod\limits_{n=1}^r n_r$ and $c_i\dfrac N{n_i}\equiv 1\mod n_i$.

Using this, we have $(b_1,b_2,b_3)=(3,2,5)$ and $(c_1,c_2,c_3)=(1,2,1)$. Hence, $x\equiv 120\equiv 0\mod 30$. Which is obviously wrong.

By trial and error, I found the answer to be $27$.

Questions:

1. How do I solve for $x$, and what went wrong in my follow through?
2. Is there an easier way to calculate $c_i\frac {N}{n_i}\equiv1\mod n_i$ (I believe this is called the inverse)?
• You've made mistakes in finding $c_i$ for each $i$. To find a multiplicative inverse (if it exists), and the extended Euclidean algorithm to keep things organised. – GNUSupporter 8964民主女神 地下教會 Feb 2 '17 at 23:24
• Yes, $c_2=-1$ or $4$, not $2$. – Thomas Andrews Feb 2 '17 at 23:28
• And $20c_3\equiv 1\pmod{11}$ so $c_3=5$. – Thomas Andrews Feb 2 '17 at 23:29

You asked for an easier (general) way. Usually it is easier two solve them a pair at a time.

${\rm mod}\ 11\!:\,\ x\equiv 5\,\Rightarrow\, x = 5+11\color{#c00}j$
${\rm mod}\ \color{#c00}5\!:\,\ \color{#c00}2\equiv x\equiv 5+11j\equiv \color{#c00}j\$ so $\,x = 5+11(\!\!\!\!\!\!\!\color{#c00}{\overbrace{2+5k}^{\large j\ \equiv\ 2\pmod{\! 5}}}\!\!\!\!\!\!\!\!)=27+55\color{#0a0}k$

${\rm mod}\ \color{#0a0}4\!:\,\ 3\equiv x\equiv 27+55k\equiv 3-k\$ so $\ \color{#0a0}{k\equiv 0}\$ so $\, x = 27+55(\!\!\!\!\!\!\!\color{#0a0}{\underbrace{0+4n}_{\large k\ \equiv\ 0\pmod{\! 4}}}\!\!\!\!\!\!\!\!) = 27+220n$

Remark $\$ This method works generally, see this answer for a proof.

It's important that $$4, 5,$$and $$11$$ are pairwise prime. Here is how I do it. (Warning. Explaining how I do it will take up much more room than what it takes to actually just do it.)

I start by making the following table

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline 55 \\ 44 \\ 20 \\ \hline \end{array}$$

Where $$55 = \dfrac{4 \cdot 5 \cdot 11}{4}=5 \cdot 11, \qquad 44 = \dfrac{4 \cdot 5 \cdot 11}{5}=4 \cdot 11, \qquad 20 = \dfrac{4 \cdot 5 \cdot 11}{11}=5 \cdot 11.$$

Note that $$4 \cdot 5 \cdot 11 = 220$$.

Then I compute the following numbers

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline 55 & 55 \pmod{4} & 55 \pmod{5} & 55 \pmod{11} \\ 44 & 44 \pmod{4} & 44 \pmod{5} & 44 \pmod{11}\\ 20 & 20 \pmod{4} & 20 \pmod{5} & 20 \pmod{11}\\ \hline \end{array}$$

Which turns out to be

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline 55 & -1 & 0 & 0 \\ 44 & 0 & -1 & 0\\ 20 & 0 & 0 & -2\\ \hline \end{array}$$

It will always happen that only the diagonal elements are non zero.

What you want to do is change each row by multiplying each number in that row by the number that will make the diagonal element equal to $$1$$. When the diagonal element is $$-1$$, this is really easy.

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline -55 & 1 & 0 & 0 \\ -44 & 0 & 1 & 0\\ 20 & 0 & 0 & -2\\ \hline \end{array}$$

It's easy to check that $$-55 \pmod 4 = 1$$ and $$-44 \pmod 5 = 1$$.

So we still need to figure out what to multiply $$-2$$ by to make the answer congruent to $$1$$ modulo $$11$$. Well $$11+1=12 = (-6)(-2)$$. So...

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline -55 & 1 & 0 & 0 \\ -44 & 0 & 1 & 0\\ -120 & 0 & 0 & 1\\ \hline \end{array}$$

The above numbers are perfectly fine; they will work; but, I would do it differently. It turns out that you can always find numbers so that the left column adds up to $$1$$. Since $$(-55) + (-44) = -99$$, then we should be able to replace $$-120$$ with $$100$$. That makes sense, since we multiplied $$20$$ by $$-6$$ and since $$-6 \equiv 5 \pmod{11}$$, we get

$$\begin{array}{c|ccc|} & 4 & 5 & 11 \\ \hline -55 & 1 & 0 & 0 \\ -44 & 0 & 1 & 0\\ 100 & 0 & 0 & 1\\ \hline \end{array}$$

The answer is then $$3(-55) + 2(-44) + 5(100) = 27 \pmod{220}$$.


text:
# Discrete Fourier Transform Matlab Code

Let's The DFT and the DTFT » Steve on Image Processing and MATLAB - MATLAB & Simulink. The wavelet and scaling filter coefficients at level j are computed by taking the inverse discrete Fourier transform (DFT) of a product of DFTs. Wolf, Integral Transforms in Science and Engineering, Plenum Press, New York, 1979). An FFT is a DFT, but is much faster for calculations. Evaluate Window Functions for the Discrete Fourier Transform The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum. MATLAB provides command for working with transforms, such as the Laplace and Fourier transforms. T—which is what the Fourier series construction ( 6. the fast Fourier transform (FFT) is a fast algorithm for computing the discrete Fourier transform. in this article: Optimal filtering in fractional Fourier. Matlab Codings For Discrete Fourier Transform Codes and Scripts Downloads Free.   The Fast Fourier Transform (FFT) is an efficient way to do the DFT, and there are many different algorithms to accomplish the FFT. In addition, what makes the DFT such a useful tool is that there are fast ways to compute it, collectively referred as Fast Fourier transforms or FFTs. discrete fractional fourier transform matlab Search and download discrete fractional fourier transform matlab open source project / source codes from CodeForge. DISCRETE FOURIER TRANSFORM - A LINEAR ALGEBRA PERSPECTIVE Harikrishnan NB. Colton March 1, 2010 1 Introduction The Discrete ourierF ransformT (DFT) is a an approximation to the ourierF ransformT for discrete signals. resolution of the dft 6. The functions X = fft(x) and x = ifft(X) implement the transform and inverse transform pair given for vectors of length by: where. Discrete-Time Fourier Transform (DTFT) Chapter Intended Learning Outcomes: (i) Understanding the characteristics and properties of DTFT (ii) Ability to perform discrete-time signal conversion between the time and frequency domains using DTFT and inverse DTFT. The output image is the square modulus of the resulting Fourier transform. Viewing an image in domains such as frequency or Hough space enables the identification of features that may not be as easily detected in the spatial domain. Spectrum Analysis with Discrete Fourier Transform. The DTFT transforms a DT sequence x[k] into a function X in the DTFT frequency domain. This volume provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z -Transform (including definition and properties, the inverse z. So don't expect the same results as MATLAB makes. It is both much faster (O(n log n) as opposed to O(n^2) with the direct method) and more stable numerically. In this tutorial numerical methods are used for finding the Fourier transform of continuous time signals with MATLAB are presented.   The Fast Fourier Transform (FFT) is an efficient way to do the DFT, and there are many different algorithms to accomplish the FFT. The Fourier Analysis Tool in Microsoft Excel Douglas A. In order to plot a Fourier Series in MATLAB, you'll have to approximate it first. TestingSpherical3DFFT. ESE 150 – Lab 04: The Discrete Fourier Transform (DFT) ESE 150 – Lab 4 Page 1 of 16 LAB 04 In this lab we will do the following: 1. I decided to demonstrate aliasing for my MATLAB example using the DFT. m - located in folder MATLAB CodeBase\NVIDIA_3DSphericalDFT - this is the 3D Spherical Polar Fourier Transform test. Description. Let's The DFT and the DTFT » Steve on Image Processing and MATLAB - MATLAB & Simulink. Using a Fast Fourier Transform Algorithm Introduction The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. Computing Fourier Series and Power Spectrum with MATLAB It turns out that taking a Fourier transform of discrete data is done by simply To take a Fourier. Formally, there is a clear distinction: 'DFT' refers to a mathematical transformation or function, regardless of how it is computed, whereas 'FFT' refers to a specific. 7 The Discrete Fourier Transform. It's finally time to start looking at the relationship between the discrete Fourier transform (DFT) and the discrete-time Fourier transform (DTFT). It is a tool for signal decomposition for further filtration, which is in fact separation of signal components from each other. Working with the Fourier transform on a computer usually involves a form of the transform known as the discrete Fourier transform (DFT). discrete-time Fourier transform (DTFT), discrete Fourier series (DFS), discrete Fourier transform (DFT) and fast Fourier transform (FFT) (ii) Understanding the characteristics and properties of DFS and DFT (iii) Ability to perform discrete-time signal conversion between the time and frequency domains using DFS and DFT and their inverse transforms. function [g] = FFTPF1D (X,binsize, f, P) Discrete Fourier Transform Low/High Pass Filter. Unlike with the Fig. To test, it creates an input signal using a Sine wave that has known frequency, amplitude, phase. It is both much faster (O(n log n) as opposed to O(n^2) with the direct method) and more stable numerically. To form the Discrete Cosine Transform (DCT), replicate x[0:N −1]but in reverse order and insert a zero between each pair of samples: → 0 12 23 y[r] Take the DFT of length 4N real, symmetric, odd-sample-only sequence. In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in Fourier analysis. Matlab Simulink Sampling Theorem and Fourier Transform Lester Liu September 26, 2012 Introduction to Simulink Simulink is a software for modeling, simulating, and analyzing dynamical systems. MatLab Code 1) Consider a 2D signal (such as an image) in an array. Here, , is the radian frequency and is the frequency in Hertz. You want the code of Discrete fourier transform in C language for your image processing program using a filter function to enhance the tiff image. after equation (7) a notation Fa is fractional fourier transform matrix, notation a is order of transform and when a=1 the matrix will be equal to simple DFT matrix. Matlab code for fast computation of the fractional Fourier transform. For more tutorials on the DFT and FFT see. We will start by recalling the definition of the Fourier transform. Short Time Fourier Transform In what follows we introduce the Short Time Fourier Transform (STFT) and its For example in matlab, the following code. t;1/is the sampling at the discrete intervals. The discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. I have written a MATLAB program code to compute Discrete Fourier Transform and Inverse Discrete Fourier Transform of a given sequence using FFT (fast fourier transform) algorithms. Fourier transform is called the Discrete Time Fourier Transform. Text figure (4. It is THE BEST sparse FFT around!!!. Continuous. A variant, the modified discrete cosine transform, or MDCT (based on the DCT-IV), is used in the MP3, AAC, Vorbis and WMA audio compression formats. Summary of the DTFT The discrete-time Fourier transform (DTFT) gives us a way of representing frequency content of discrete-time signals. e ^jwt + Rb. To illustrate how the Fourier transform captures similarity between a signal and sinusoids of different frequencies, the following MATLAB code analyzes a signal consisting of two sinusoids of 4 and 8 Hertz (Hz) corrupted by additive noise using the discrete Fourier transform. Popularity of Hartley. For now, it is useful and informative to demonstrate the derivation of the. The marked data points are taken from a horizontal cross-section of the output image. [Artyom Grigoryan; Merughan M Grigoryan] -- "The book is devoted to the problem of image reconstruction from a finite number of projections. The whole point of the FFT is speed in calculating a DFT. Matlab checks whether there is a builtin routine named a; Matlab looks in the path for a function a. Members wish to be useful > Signal Processing > Transforms > Discrete. Introduction A linear and time-invariant system can be represented using its response to the unit sample sequence. Charles Bouman and Prof. Information and translations of discrete Fourier transform in the most comprehensive dictionary definitions resource on the web. This is in contrast to the DTFT that uses discrete time, but converts to continuous frequency. The tools include MatLab, LabVIEW, PSpice (a simulation software), and the Lab test. In dimensions, the data is specified by a list nested levels deep. The solution shows step-by-step calculation of discrete time Fourier transform of a sequence. Ask Question. Fast complexiﬁed quaternion Fourier transform Salem Said† Nicolas Le Bihan† Stephen J. Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS320 DSP Platform Robert Matusiak Digital Signal Processing Solutions ABSTRACT The Fast Fourier Transform (FFT) is an efficient computation of the Discrete Fourier Transform (DFT) and one of the most important tools used in digital signal processing applications. Software Metapapers Matlab Code for the Discrete Hankel Transform Authors: Natalie Baddour , University of Ottawa, CA Profiles: iD About Natalie Natalie Baddour is an associate professor in the Department of Mechanical Engineering at the University of Ottawa, Canada. Write a matlab program to input an image. Fast Transforms in Audio DSP; Related Transforms. ESE 150 – Lab 04: The Discrete Fourier Transform (DFT) ESE 150 – Lab 4 Page 1 of 16 LAB 04 In this lab we will do the following: 1. Discrete Fourier transform Plot. dft and sinusoids 7. Discrete-Time Fourier Transform / Solutions S11-5 for discrete-time signals can be developed. If the first argument contains a symbolic function, then the second argument must be a scalar. In dimensions, the data is specified by a list nested levels deep. Following is an introduction to Fourier Series, Fourier Transforms, the Discrete Fourier Transform (for calculation of Fourier Series coefficients with a computer) and ways of. Sketch a graph of this function. The functions X = fft(x) and x = ifft(X) implement the transform and inverse transform pair given for vectors of length by: where. DFT transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function (which is often a function in the time domain). A collection of sparse Fourier transform codes developed by faculty at MSU. An FFT is a "Fast Fourier Transform". Arguably the most beneficial aspect of a Fourier series is that it is possible to deconstruct a complex wave into a smaller series of sine and cosine waves. As shown in the image below. We will start by recalling the definition of the Fourier transform. Note that the function is long in the y-direction and short in the x-direction. wav file that I uploaded to Matlab and stored as a vector Y using the wavread function. Y = fft(X) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm. If X is a vector, then fft(X) returns the Fourier transform of the vector. The discrete Fourier transform (DFT) is a basic yet very versatile algorithm for digital signal processing (DSP). These numbers may arise, for example, as a discretely sampled values of an analog function sampled over some period window and then. To explain it clearly, have a look at this easy example : Lets consider a function$f(t) = |sin(\pi t)|$ on the interval[math] [\dfrac{-1}{2}, \dfrac{1}{2. It not only introduces the four Fourier analysis tools, CTFS (continuous-time Fourier series), CTFT (continuous-time Fourier transform), DFT (discrete-time Fourier transform), and DTFS (discrete-time Fourier series), but also illuminates the relationship among them so that the readers can realize why only the DFT of the four tools is used for. is an th root of unity. 4) %Matlab Code %Matlab Code close all; clear all;. Matlab code for fast computation of the fractional Fourier transform. 2 FOURIER TRANSFORMS 8. Usually, you also need to apply a window function to the captured signal before taking the DFT [1 - 3]. Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB ® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. This DHT possesses orthogonality properties which lead to invertibility and also possesses the standard set of discrete shift, modulation, multiplication and convolution rules. Z-Transform - Properties; Z-Transform - Existence; Z-Transform - Inverse; Z-Transform - Solved Examples; Discrete Fourier Transform; DFT - Introduction; DFT - Time Frequency Transform; DTF - Circular Convolution; DFT - Linear Filtering; DFT - Sectional Convolution; DFT - Discrete Cosine Transform; DFT - Solved Examples; Fast Fourier Transform. In today's post, I will show you how to perform a two-dimensional Fast Fourier Transform in Matlab. FFT is finite Fourier transform, its fast when the length of vector on which is evaluated is ~ to 2^N where N is an. In this tutorial numerical methods are used for finding the Fourier transform of continuous time signals with MATLAB are presented. In this case the transform and its inverse are = = ∑ =. Often we are confronted with the need to generate simple, standard signals ( sine, cosine , Gaussian pulse , squarewave , isolated rectangular pulse , exponential decay, chirp signal ) for. Hello there, anyone knows how to write a matlab code to calculate the discrete fourier series and its inverse given by: where fft is "fast fourier transform", and. the Matlab function "fft2") • Reordering puts the spectrum into a "physical" order (the same as seen in optical Fourier transforms) (e. For a more efficient but less obvious program, the discrete Fourier transform can be computed using the command fft which performs a Fast Fourier Transform of a sequence of numbers. The DFT has its own exact Fourier theory, which is the main focus of this book. we visually analyze a Fourier transform by computing a Fourier spectrum (the magnitude of F(u,v)) and display it as an image. in this article: Optimal filtering in fractional Fourier. If X is a matrix, fft returns the Fourier transform. I have to denoise an ECG siganl using fourier transform. The DFT provides an efficient way to calculate the time-domain convolution of two signals. Later it calculates DFT of the input signal and finds its frequency, amplitude, phase to compare. Fast Fourier Transform v9. I need the matlab code for this problem. The following Matlab project contains the source code and Matlab examples used for discrete fourier transform of a finite sequence. Discrete Fourier Transform MATLAB Code for DFT without using fft function Important to note this that this is a function file not script, you need to pass parameters to execute this program. MATLAB has three functions to compute the DFT: 1. It can be called using "fft(Y)" where Y is the desired array of data. we visually analyze a Fourier transform by computing a Fourier spectrum (the magnitude of F(u,v)) and display it as an image. I find a strange grid like phase in the Fourier plane. m - located in folder MATLAB CodeBase\NVIDIA_3DSphericalDFT - this is the 3D Spherical Polar Fourier Transform test. Sketch a graph of this function. Because the discrete Fourier transform separates its input into components that contribute at discrete frequencies, it has a great number of applications in digital signal processing, e. Later it calculates DFT of the input signal and finds its frequency, amplitude, phase to compare. In this tutorial we will study the formula for computing the discrete Fourier transform (DFT) and numerically study the DFT on a short signal (only a few samples) in order to keep track on the indices in the FT formula (which most people consider complicated and abstract when working with long signals). Discrete Fourier Transform (DFT) Recall the DTFT: X(ω) = X∞ n=−∞ x(n)e−jωn. The DFT is normally encountered in practice as a Fast Fourier Transform (FFT), which is a high-speed algorithm for computing the DFT. For more tutorials on the DFT and FFT see. t/: Now we need three facts (see section 6. Write a matlab program to input an image. Using the inverse Fourier transformation the time series signal can be reconstructed from its frequency-domain representation. The MATLAB® environment provides the functions fft and ifft to compute the discrete Fourier transform and its inverse, respectively. Given a function x(t) for , its Fourier transform is given by , subject to the usual existence conditions for the integral. Fourier transform is one of the various mathematical transformations known which is used to transform signals from time domain to frequency domain. Arguably the most beneficial aspect of a Fourier series is that it is possible to deconstruct a complex wave into a smaller series of sine and cosine waves. Today I want to start getting "discrete" by introducing the discrete-time Fourier transform (DTFT). It also includes the Matlab codes and plots implementation. To perform a two dimensional Fourier transform, one can first transform all rows, and then all columns. The DFT is simply an invertible linear map from $\mathbb{C}^n$ to itself, i. The demo below performs the discrete Fourier transform on the function f(x). Description. zero padding 3. It is a periodic function and thus cannot represent any arbitrary function. Following is an introduction to Fourier Series, Fourier Transforms, the Discrete Fourier Transform (for calculation of Fourier Series coefficients with a computer) and ways of. a Matlab code for 3D and using the discrete Fourier transform may either discard high-frequency components. 1 representation of periodic sequences: the discrete fourier series 8. 2 the fourier transform of periodic signals 8. TestingSpherical3DFFT. Introduction FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i. 1 Representation of Aperiodic Signals: The discrete-Time Fourier Transform 5. Two ‐ dimensional discrete Fourier transforms are often used in image processing. Y = fft(X) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm. The demo below performs the discrete Fourier transform on the function f(x). 1 DIODE CHARACTERISTICS 9. DISCRETE FOURIER TRANSFORM - A LINEAR ALGEBRA PERSPECTIVE Harikrishnan NB. In case of digital images are discrete. Colton March 1, 2010 1 Introduction The Discrete ourierF ransformT (DFT) is a an approximation to the ourierF ransformT for discrete signals. Let be the continuous signal which is the source of the data. Yip, Discrete cosine transform: algorithms, advantages, applications. Define x[n/k], if n is a multiple of k, 0, otherwise X(k)[n] is a "slowed-down" version of x[n] with zeros interspersed.   The Discrete Fourier Transform (DFT) transforms discrete data from the sample domain to the frequency domain. We start with a brief overview on the windowed Fourier transform (WFT), also called short-time Fourier transform. Discrete Fourier Series: In physics, Discrete Fourier Transform is a tool used to identify the frequency components of a time signal, momentum distributions of particles and many other applications. For the input sequence x and its transformed version X (the discrete-time Fourier transform at equally spaced frequencies around the unit circle), the two functions implement the relationships. Finite summation: , for integers N ≥ 1Fast-Fourier Transform: A way to compute discrete Fourier transform and its inverse. As of right now I’ve written the code to do 1. we visually analyze a Fourier transform by computing a Fourier spectrum(the magnitude of F(u,v)) and display it as an image. For the input sequence x and its transformed version X (the discrete-time Fourier transform at equally spaced frequencies around the unit circle), the two functions implement the relationships. It sup-ports linear and nonlinear systems, modeled in continuous time, sampled time or hybrid of two. ^2 (source code: somb. The DFT provides an efficient way to calculate the time-domain convolution of two signals. In Chapter 11, we introduced the discrete-time Fourier transform (DTFT) that provides us with alternative representations for DT sequences. TestingSpherical3DFFT. We would like the Fourier transform of this signal. 2) 1D Discrete Fourier Transform %Matlab Code (4. The Discrete Fourier Transform (DFT) is a numerical approximation to the Fourier transform. Formally, there is a clear distinction: 'DFT' refers to a mathematical transformation or function, regardless of how it is computed, whereas 'FFT' refers to a specific. The solid curve is the ideal function, which was generated from somb(r/16). A discrete transform is a transform whose input and output values are discrete samples, making it convenient for computer manipulation. Fourier Transforms and Fast Fourier Transforms. Discrete Fourier transform (DFT) The discrete Fourier transform (DFT) is the digital version of Fourier transform, which is used to analyze digital signals. The solution shows step-by-step calculation of discrete time Fourier transform of a sequence. Transforms are used in science and engineering as a tool for simplifying analysis and look at data from another angle. Working with the Fourier transform on a computer usually involves a form of the transform known as the discrete Fourier transform (DFT). Using a Fast Fourier Transform Algorithm Introduction The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. php(143) : runtime-created function(1) : eval()'d code(156) : runtime-created. Need FFT Code for Matlab (not built in). To compute the FFT of a sequence x[n] which is stored in the vector x, use the command X = fft(x) Used in this way, the command fft is interchangeable with the. zero padding 3. Conventional fft ignores negative frequencies isn't it ? What I like to have is in this form Rf. Later it calculates DFT of the input signal and finds its frequency, amplitude, phase to compare. Write a matlab program to input an image. MATLAB PROGRAM TO IMPLEMENT THE PROPERTIES OF DISCRETE FOURIER TRANSFORM (DFT) - FREQUENCY SHIFT PROPERTY %Discrete time fourier transform i want matlab code. Mathematics of the DFT Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples. Sparse Fast Fourier Transform : The discrete Fourier transform (DFT) is one of the most important and widely used computational tasks. Discrete Fourier Transform Description| How it works| Gallery 1| Gallery 2 This is a powerful tool that will convert a given signal from the time domain to the frequency domain. ) DMSFT, implemented by Ruochuan Zhang. Hello there, anyone knows how to write a matlab code to calculate the discrete fourier series and its inverse given by: where fft is "fast fourier transform", and. A digital Fourier transform (DFT) is a transformation of n points. The output is a plot of the data points and the function fit, the Fourier coefficients and the periodogram giving the power spectrum. Week 8: Discrete Fourier Transform and Fast Fourier Transform Algorithms (Week 2) Date Section Name Sign Time spent outside lab [ %] [ %] Grading Rubric (Fall 2019) below lacks in meets all expectations some respect expectations Completeness of the report Organization of the report One-sided, with cover sheet, answers are in the same order as. The Fourier transform has long been used for characterizing linear systems and for identifying the frequency components making up a continuous waveform. DTFT is not suitable for DSP applications because •In DSP, we are able to compute the spectrum only at speciﬁc. Matlab Simulink Sampling Theorem and Fourier Transform Lester Liu September 26, 2012 Introduction to Simulink Simulink is a software for modeling, simulating, and analyzing dynamical systems. 5 sampling the fourier transform (point of sampling) 8. Get this from a library! Image processing : tensor transform and discrete tomography with MATLAB. Discrete Time Fourier Transform (DTFT) in MATLAB - Matlab Tutorial Online Course - Uniformedia. ) DMSFT, implemented by Ruochuan Zhang. Such an analysis oﬀers a more detailed look to signals with time-varying frequency content. • A secondary purpose of this lab is to introduce you to the tools and procedures that will be required for successful completion of the Communications Labs. in this article: Optimal filtering in fractional Fourier. The FFT is an algorithm for computing a DFT that operates in N log2(N) complexity versus the expected N2 complexity of a naive implementation of a DFT. Description. Software Metapapers Matlab Code for the Discrete Hankel Transform Authors: Natalie Baddour , University of Ottawa, CA Profiles: iD About Natalie Natalie Baddour is an associate professor in the Department of Mechanical Engineering at the University of Ottawa, Canada. I need some MATLAB code for 2-D DFT(2-dimensional Discrete Fourier Transform) of an image and some examples to prove its properties like separability, translation, and rotation. There are two types of fourier transforms namely, discrete and inverse discrete. Discrete-Time Fourier Transform (DTFT) Chapter Intended Learning Outcomes: (i) Understanding the characteristics and properties of DTFT (ii) Ability to perform discrete-time signal conversion between the time and frequency domains using DTFT and inverse DTFT. The computational complexity of the DFT is N 2 whereas its (N)log 2 N for the FFT, where N is the number of samples of the the time domain signal. A Fourier Transform will break apart a time signal and will return information about the frequency of all sine waves needed to simulate that time signal. 3 properties of the discrete fourier series 8. MATLAB has three functions to compute the DFT: 1. This document describes the Discrete Fourier Transform (DFT), that is, a Fourier Transform as applied to a discrete complex valued series. Exercise 6: Find the Discrete Fourier Transform (DFT) of a signal f(t) by using the Fast Fourier Transform (FFT) algorithm in MATLAB. 4) %Matlab Code %Matlab Code close all; clear all;. You can also view the old lecture notes from Autumn 2000 offering of random signals, z-transform [ PDF] [ MATLAB code] 10/15/2001 Discrete Fourier Transform. It converts a signal into individual spectral components and thereby provides frequency information about the signal. This is the first tutorial in our ongoing series on time series spectral analysis. Discrete Fourier Transform. Matlab Code for Circular Convolution. discrete fourier Transform. This article will walk through the steps to implement the algorithm from scratch. Y = fft(X) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm. we visually analyze a Fourier transform by computing a Fourier spectrum(the magnitude of F(u,v)) and display it as an image. x/e−i!x dx and the inverse Fourier transform is. An image transform can be applied to an image to convert it from one domain to another. function [g] = FFTPF1D (X,binsize, f, P) Discrete Fourier Transform Low/High Pass Filter. dftmtx takes the FFT of the identity matrix to generate the transform matrix. Sampling Signals Overview: We use the Fourier transform to understand the discrete sampling and re-sampling of signals. discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. We got to this definition, using square brackets to denote list indexing (or vector indexing, whatever):. An FFT is a DFT, but is much faster for calculations. It is THE BEST sparse FFT around!!!. Although, the process of crossing the border between these two worlds (time and. The Fast Fourier Transform (FFT) is one of the most important algorithms in signal processing and data analysis. The solution shows step-by-step calculation of discrete time Fourier transform of a sequence. This is a fast, stable, noise robust, and *fully discrete* improvement on the ideas in GFFT below. Now arises the situation what do we do for aperiodic signals. In order to plot a Fourier Series in MATLAB, you'll have to approximate it first. Gheorghe TODORAN, Rodica HOLONEC and Ciprian IAKAB. As the name suggests, it's much faster. In image processing, the 2D Fourier Transform allows one to see the frequency spectrum of the data in both. Evaluating Fourier Transforms with MATLAB In class we study the analytic approach for determining the Fourier transform of a continuous time signal. How to do a Fast Fourier Transform (FFT) with Correct Amplitude Output in Matlab ; In this tutorial, we will go over how to do a fast Fourier transform on a time domain signal properly using Matlab. For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT. Construction and Properties of Canonical Transforms (chapter 9 of K. Discrete-TimeFourierTransform: x[n],X(ej How does the discrete Fourier transform relate to the other transforms? Firstofall,the 4 Matlab and the FFT. the Matlab function "fft2") • Reordering puts the spectrum into a "physical" order (the same as seen in optical Fourier transforms) (e. after equation (7) a notation Fa is fractional fourier transform matrix, notation a is order of transform and when a=1 the matrix will be equal to simple DFT matrix. Discrete Fourier Transform and Fast Fourier Transform Algorithms (Week 1) By Prof. Discrete Fourier transform (DFT) Alejandro Ribeiro January 28, 2019 Let x : [0, N 1] !C be a discrete signal of duration N and having elements x(n) for n 2[0, N 1]. m - located in folder MATLAB CodeBase\NVIDIA_3DSphericalDFT - this is the 3D Spherical Polar Fourier Transform test. 5 Learning Objectives: To make the students familiar with concept of DFT and IDFT with the use of MATLAB. The MATLAB® environment provides the functions fft and ifft to compute the discrete Fourier transform and its inverse, respectively. File Exchange fractional Fourier transform matlab source code. Try this code %Read Input Image Input_Image=imread(‘rose. It is used in digital cameras. I agree with Steven that the discrete fourier transform operations are vector operations. Computing Fourier Series and Power Spectrum with MATLAB It turns out that taking a Fourier transform of discrete data is done by simply To take a Fourier. The 2D Fourier Transform is an indispensable tool in many fields, including image processing, radar, optics and machine vision. I realize that this can be a separable operation, so I am creating a matrix for 1D DFT and multiplying it with the columns of an input image and then the rows of the image. Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS320 DSP Platform Robert Matusiak Digital Signal Processing Solutions ABSTRACT The Fast Fourier Transform (FFT) is an efficient computation of the Discrete Fourier Transform (DFT) and one of the most important tools used in digital signal processing applications. For example in a basic gray scale image values usually are between zero and 255. And also brush up. It's finally time to start looking at the relationship between the discrete Fourier transform (DFT) and the discrete-time Fourier transform (DTFT). Toggle Main Navigation. The standard algorithm for the MODWT implements the circular convolution directly in the time domain. Search File Exchange. Matlab code for fast computation of the fractional Fourier transform. zip file (10 KB) How to use The use of this app is quite similar to the Function Calculus Tool. Arguably the most beneficial aspect of a Fourier series is that it is possible to deconstruct a complex wave into a smaller series of sine and cosine waves. 5 sampling the fourier transform (point of sampling) 8. The following Matlab project contains the source code and Matlab examples used for discrete fourier transform. Meaning of discrete Fourier transform. Discrete Time Fourier Transform (DTFT) in MATLAB - Matlab Tutorial Online Course - Uniformedia. Note that this function will only calculate the forward transform of the y-values of the data and. Recently, the theory of a Discrete Hankel Transform was proposed that follows the same path as the Discrete Fourier/Continuous Fourier transform. How to plot DFT (Discrete Fourier Transform) and IDFT (Inverse Discrete Fourier Transform) using MATLAB. The FFT is an algorithm for computing a DFT that operates in N log2(N) complexity versus the expected N2 complexity of a naive implementation of a DFT. The DFT has its own exact Fourier theory, which is the main focus of this book. A Lookahead: The Discrete Fourier Transform. In order to plot a Fourier Series in MATLAB, you'll have to approximate it first. MATLAB/octave provide the built-in functions fft and the inverse ifft. I am trying to write a matlab code for some calculations based on Discrete fractional fourier transform. The Discrete Fourier Transform (DFT) transforms discrete data from the sample domain to the frequency domain. Discrete Fourier transform Plot. Evaluate Window Functions for the Discrete Fourier Transform The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum. If you are already familiar with it, then you can see the implementation directly. DISCRETE FOURIER TRANSFORM (DFT) AND THE FAST FOURIER TRANSFORM (FFT): This lecture details the algorithm used for constructing the FFT and DFT representations using efficient computation. The MATLAB® environment provides the functions fft and ifft to compute the discrete Fourier transform and its inverse, respectively. If inverse is TRUE, the (unnormalized) inverse Fourier transform is returned, i. We would like the Fourier transform of this signal. Mireille Boutin Fall 2019 1 Introduction This is the ﬁrst week of a two week laboratory that covers the Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) methods. Write a MATLAB CODE ONLY!!! function [X] = dtft(x,n,w) % Computes Discrete-time Fourier Transform % [X] = dtft(x,n,w) % X = DTFT values are computed at w frequencies. Although, the process of crossing the border between these two worlds (time and. MATLAB provides command for working with transforms, such as the Laplace and Fourier transforms. Frequency spectrum conversions for signals include the Fourier Transform(FT), Discrete Fourier Transform(DFT), Fast Fourier Transform(FFT), Laplace Transform, Z-Transform…ect. The MATLAB® environment provides the functions fft and ifft to compute the discrete Fourier transform and its inverse, respectively. I have to denoise an ECG siganl using fourier transform. This class of Fourier Transform is sometimes called the Discrete Fourier Series, but is most often called the Discrete Fourier Transform. Summary of the DTFT The discrete-time Fourier transform (DTFT) gives us a way of representing frequency content of discrete-time signals. It describes in detail 2-D discrete Fourier transform, including properties, fast algorithms, and. It is usually implemented using the Fast Fourier Transform (FFT). In this case the transform and its inverse are = = ∑ =. Like the ourierF ransform,T the DFT enables us to determine the frequency-domain representation, in the form of ourierF coe cients, of a time-domain signal. When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT). Matlab Codings For Discrete Fourier Transform Codes and Scripts Downloads Free. Fourier Transform of aperiodic and periodic signals - C. after equation (7) a notation Fa is fractional fourier transform matrix, notation a is order of transform and when a=1 the matrix will be equal to simple DFT matrix. This DHT possesses orthogonality properties which lead to invertibility and also possesses the standard set of discrete shift, modulation, multiplication and convolution rules. An image transform can be applied to an image to convert it from one domain to another. If F= E E 1 is this decomposition then Fa = E aE 1 is the corresponding discrete fractional Fourier transform.