Comments on: Understanding the Fourier transform [...] [...] [...] [...]

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By: Today in WoW: Friday, Aug. 26, 2011/2011/05/17/understanding-the-fourier-transform/#comment-6414 Today in WoW: Friday, Aug. 26, 2011 Sat, 27 Aug 2011 11:48:40 +0000 You are my hero. Thank you for article! You are my hero. Thank you for article!

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By: pix/2011/05/17/understanding-the-fourier-transform/#comment-6304 pix Sat, 25 Jun 2011 00:17:49 +0000 [...] example: there was an excellent article on the Fourier Transform. One of the best [...] [...] example: there was an excellent article on the Fourier Transform. One of the best [...]

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By: The Fourier transform, the FFT and the DFT – Coding Miscellanea/2011/05/17/understanding-the-fourier-transform/#comment-5036 The Fourier transform, the FFT and the DFT – Coding Miscellanea Tue, 31 May 2011 21:37:07 +0000 I'm sorry I didn't mean to say it that mean. However, your students might be leaving your courses with only knowledge, and hardly any understanding, if that's how you explain Euler's formula to them. I’m sorry I didn’t mean to say it that mean. However, your students might be leaving your courses with only knowledge, and hardly any understanding, if that’s how you explain Euler’s formula to them.

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By: Christeph/2011/05/17/understanding-the-fourier-transform/#comment-5005 Christeph Tue, 31 May 2011 02:28:11 +0000 Applying consistency(e) to(^) complexity(i) gives continuity (so spin can occur). If that doesn't help you there are other mind trick approaches I can tell you about. Applying consistency(e) to(^) complexity(i) gives continuity (so spin can occur).

If that doesn’t help you there are other mind trick approaches I can tell you about.

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By: Michael/2011/05/17/understanding-the-fourier-transform/#comment-5000 Michael Tue, 31 May 2011 00:20:24 +0000 Stuart - I explain stuff visually all day long, and have bupkus knowledge of math. I just wanted to say "NICE JOB" crafting an explanation. Very helpful and inspiring. Stuart – I explain stuff visually all day long, and have bupkus knowledge of math. I just wanted to say “NICE JOB” crafting an explanation. Very helpful and inspiring.

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By: The Fourier Series/2011/05/17/understanding-the-fourier-transform/#comment-4783 The Fourier Series Tue, 24 May 2011 01:58:29 +0000 A sound of "Fourier transform" always made me tremble, but not after I read this!!! I think what will also help people really understand what is going on are a couple of simple graphs that show a signal with only one frequency to see how it translates to a bead/rod image. Thanks for such a great post! A sound of “Fourier transform” always made me tremble, but not after I read this!!!

I think what will also help people really understand what is going on are a couple of simple graphs that show a signal with only one frequency to see how it translates to a bead/rod image.

Thanks for such a great post!

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By: Cristián Arenas Ulloa/2011/05/17/understanding-the-fourier-transform/#comment-4745 Cristián Arenas Ulloa Mon, 23 May 2011 06:38:10 +0000 Job well done sir. Even complex things have simple explanations if you find the right way to see it. This was the best treatment i've seen of FFT, and I will likely never forget it. Job well done sir. Even complex things have simple explanations if you find the right way to see it. This was the best treatment i’ve seen of FFT, and I will likely never forget it.

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By: machinarium/2011/05/17/understanding-the-fourier-transform/#comment-4652 machinarium Fri, 20 May 2011 16:17:09 +0000 Man, I owe you a beer for this! Great work! Although I think I would have a slight suggestion how to make the description a bit better, how about describing the rotation part like this: Now imagine that you pull the time axis towards your direction, so that it points right into your eyes. Secondly you point a flashlight in it's direction and a screen behind the access, so that the bead which travels on our signal gets projected on the screen. Tracing that dot, we get the pictures you've created. Once again, awesome work! Man, I owe you a beer for this! Great work!
Although I think I would have a slight suggestion how to make the description a bit better, how about describing the rotation part like this:
Now imagine that you pull the time axis towards your direction, so that it points right into your eyes.
Secondly you point a flashlight in it’s direction and a screen behind the access, so that the bead which travels on our signal gets projected on the screen.
Tracing that dot, we get the pictures you’ve created.

Once again, awesome work!

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By: Chui Tey/2011/05/17/understanding-the-fourier-transform/#comment-4603 Chui Tey Thu, 19 May 2011 23:06:16 +0000 Article about Fourier transform in Wikipedia should reference this page! Article about Fourier transform in Wikipedia should reference this page!

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By: Stuart Riffle/2011/05/17/understanding-the-fourier-transform/#comment-4573 Stuart Riffle Thu, 19 May 2011 16:47:52 +0000

…and let me know if it helps? (Actually, let me know if it doesn’t help too. A lot of people are having trouble with the description, and I’m having a hard time finding the right combination of words to paint the picture).

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By: Stuart Riffle/2011/05/17/understanding-the-fourier-transform/#comment-4571 Stuart Riffle Thu, 19 May 2011 16:41:45 +0000 I made some animations to explain the spinning thing. http://fixplz.blourp.com/blog/=dfts I made some animations to explain the spinning thing.

As a mathematician, I have to say, you did a great job of explaining the Fourier. As a mathematician, I have to say, you did a great job of explaining the Fourier.

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By: Stuart Riffle/2011/05/17/understanding-the-fourier-transform/#comment-4553 Stuart Riffle Thu, 19 May 2011 12:05:55 +0000
FFT implementation instead. It does the same thing, but much faster.

]]> By: machinarium/2011/05/17/understanding-the-fourier-transform/#comment-4548 machinarium Thu, 19 May 2011 11:17:31 +0000 after 10 revolution? I don’t get it.

Thank you

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By: kkk/2011/05/17/understanding-the-fourier-transform/#comment-4507 kkk Thu, 19 May 2011 00:54:53 +0000 Yep, the "positive" end of the rod would always stay the same. Cheers, -Stuart Yep, the “positive” end of the rod would always stay the same.

Cheers,
-Stuart

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By: Shawn/2011/05/17/understanding-the-fourier-transform/#comment-4463 Shawn Wed, 18 May 2011 16:49:14 +0000 Thanks Shawn! I only meant that when we use real numbers as inputs, the imaginary part is just set to zero. I didn't mean to throw away the imaginary component of the output! As you said, that won't work. I'll see what I can do to make that more clear. Thank you for pointing that out. Thanks Shawn! I only meant that when we use real numbers as inputs, the imaginary part is just set to zero. I didn’t mean to throw away the imaginary component of the output! As you said, that won’t work. I’ll see what I can do to make that more clear. Thank you for pointing that out.

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By: Shawn/2011/05/17/understanding-the-fourier-transform/#comment-4456 Shawn Wed, 18 May 2011 16:29:47 +0000 Thank you for this explanation - I already knew what the Fourier transform did, but I find this a much clearer way of thinking about it! Thank you for this explanation – I already knew what the Fourier transform did, but I find this a much clearer way of thinking about it!

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By: Jedd Haberstro/2011/05/17/understanding-the-fourier-transform/#comment-4436 Jedd Haberstro Wed, 18 May 2011 12:46:03 +0000 Yes! What a brilliant idea! PLEASE let this catch on as a way to explain what's happening in a formula. Well done for an excellent article. This proves that crafting an explanation has an exponential impact on understanding. Writers, take note! Yes! What a brilliant idea! PLEASE let this catch on as a way to explain what’s happening in a formula. Well done for an excellent article. This proves that crafting an explanation has an exponential impact on understanding. Writers, take note!

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By: Carl Gauss/2011/05/17/understanding-the-fourier-transform/#comment-4428 Carl Gauss Wed, 18 May 2011 11:27:20 +0000 Simply excellent! I have studied math at a very high level in France for years and nobody ever explained me that! Thank you so much! Simply excellent!

I have studied math at a very high level in France for years and nobody ever explained me that!

Thank you so much!

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By: vahid/2011/05/17/understanding-the-fourier-transform/#comment-4425 vahid Wed, 18 May 2011 11:09:15 +0000 Excellent bit of writing! Thanks very much! Excellent bit of writing! Thanks very much!

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By: ahfoo/2011/05/17/understanding-the-fourier-transform/#comment-4401 ahfoo Wed, 18 May 2011 05:42:34 +0000 Hehe, the animation is cool to look at :) ...So the 3 animations at the bottom are the "spinning rods" spinning at different frequencies using the wave on top as their function. The interesting one is on the bottom right, which spins at the same frequency of one of the wave components of the original function. And, as you can see, the figure created is not perfectly symmetrical, which means that there is an energy level being detected at that frequency. Hehe, the animation is cool to look at :)

…So the 3 animations at the bottom are the “spinning rods” spinning at different frequencies using the wave on top as their function. The interesting one is on the bottom right, which spins at the same frequency of one of the wave components of the original function. And, as you can see, the figure created is not perfectly symmetrical, which means that there is an energy level being detected at that frequency.

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By: ahfoo/2011/05/17/understanding-the-fourier-transform/#comment-4399 ahfoo Wed, 18 May 2011 05:28:19 +0000 Hey great article! If you genuinely don't know how Euler's formula works, check out the Taylor expansion of e^(ix) and compare it with those of i*sin(x) and cos(x). You should see that the terms with odd powers of (ix) coincide with the terms of i*sin(x) and those with even powers coincide with those of cos(x). Hey great article! If you genuinely don’t know how Euler’s formula works, check out the Taylor expansion of e^(ix) and compare it with those of i*sin(x) and cos(x). You should see that the terms with odd powers of (ix) coincide with the terms of i*sin(x) and those with even powers coincide with those of cos(x).

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By: urtubia/2011/05/17/understanding-the-fourier-transform/#comment-4392 urtubia Wed, 18 May 2011 04:05:50 +0000

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By: Stuart Riffle/2011/05/17/understanding-the-fourier-transform/#comment-4385 Stuart Riffle Wed, 18 May 2011 03:06:19 +0000 This was very good. I'm an electrical engineering student at university, and I am specializing in signals. This is a phenomenal explanation, since my understanding was always more mathematical. It's clear that you picked this up yourself, which makes it a naturally more intuitive understanding. I'll be using it whenever students come into the tutoring room for help with the DFT. :) This was very good. I’m an electrical engineering student at university, and I am specializing in signals. This is a phenomenal explanation, since my understanding was always more mathematical. It’s clear that you picked this up yourself, which makes it a naturally more intuitive understanding. I’ll be using it whenever students come into the tutoring room for help with the DFT. :)

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By: Chris/2011/05/17/understanding-the-fourier-transform/#comment-4374 Chris Wed, 18 May 2011 01:13:00 +0000 Thank you, that's a good idea. Thank you, that’s a good idea.

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By: Bob/2011/05/17/understanding-the-fourier-transform/#comment-4370 Bob Wed, 18 May 2011 00:52:46 +0000 and then show where they end up on the graph below it, when spun.

Just a thought.

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By: Stuart Riffle/2011/05/17/understanding-the-fourier-transform/#comment-4361 Stuart Riffle Tue, 17 May 2011 23:16:22 +0000

Cheers,
-Stuart

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By: Tim Fellows/2011/05/17/understanding-the-fourier-transform/#comment-4357 Tim Fellows Tue, 17 May 2011 22:39:01 +0000 Exactly. When we spin at 3 revolutions per second, we are able to detect the energy at 3 Hz because the graph is skewed. I was just trying to show that when there's no energy at 3 Hz, the graph is no longer skewed. The first graphs are exactly the same signal, just spun at different speeds. For the last graph, I modified the signal to show what it would look like. Exactly. When we spin at 3 revolutions per second, we are able to detect the energy at 3 Hz because the graph is skewed. I was just trying to show that when there’s no energy at 3 Hz, the graph is no longer skewed.

The first graphs are exactly the same signal, just spun at different speeds. For the last graph, I modified the signal to show what it would look like.

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