Cool, but unreadable as a colorblind person with deuteranopia.
The Fourier Transform, explained in one sentence (2014)
161–170 of 171 posts
Re: The Fourier Transform, explained in one sentence (2014)
#162Honestly, it's not so bad. It's easy to pick any such attempt apart. This is close to my favorite pithy way of explaining it, too, which is to break it down component-wise using the idea of filter banks. It's not a single sentence, but here's what I tend to say: Any signal—like sounds or electrical signals, or even images—can be thought of as having a certain amount of 'energy' at any choice of frequency. This makes…
To be honest I think your explanation misses the point in two important ways. First, the Fourier transform does not just measure the 'energy' or amplitude of a single wave; it must also take into account its phase. Second, complex exponentials are in no way an essential ingredient for defining the Fourier transform. We just work with them for computational simplicity, essentially because exp(ix) exp(iy) = exp(i(x+y))…
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Re: The Fourier Transform, explained in one sentence (2014)
#163Honestly, it's not so bad. It's easy to pick any such attempt apart. This is close to my favorite pithy way of explaining it, too, which is to break it down component-wise using the idea of filter banks. It's not a single sentence, but here's what I tend to say: Any signal—like sounds or electrical signals, or even images—can be thought of as having a certain amount of 'energy' at any choice of frequency. This makes…
As someone who still doesn't understand the Fourier Transform, this explanation doesn't help, nor does the article's. As a complete noob, your explanation shows off what you know but doesn't help newcomers learn it.
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Re: The Fourier Transform, explained in one sentence (2014)
#164Honestly, it's not so bad. It's easy to pick any such attempt apart. This is close to my favorite pithy way of explaining it, too, which is to break it down component-wise using the idea of filter banks. It's not a single sentence, but here's what I tend to say: Any signal—like sounds or electrical signals, or even images—can be thought of as having a certain amount of 'energy' at any choice of frequency. This makes…
As someone who still doesn't understand the Fourier Transform, this explanation doesn't help, nor does the article's. As a complete noob, your explanation shows off what you know but doesn't help newcomers learn it.
Give this a try: https://news.ycombinator.com/item?id=11354730
Re: The Fourier Transform, explained in one sentence (2014)
#165Honestly, it's not so bad. It's easy to pick any such attempt apart. This is close to my favorite pithy way of explaining it, too, which is to break it down component-wise using the idea of filter banks. It's not a single sentence, but here's what I tend to say: Any signal—like sounds or electrical signals, or even images—can be thought of as having a certain amount of 'energy' at any choice of frequency. This makes…
To be honest I think your explanation misses the point in two important ways. First, the Fourier transform does not just measure the 'energy' or amplitude of a single wave; it must also take into account its phase. Second, complex exponentials are in no way an essential ingredient for defining the Fourier transform. We just work with them for computational simplicity, essentially because exp(ix) exp(iy) = exp(i(x+y))…
I agree with these criticisms. Really, my goal when I talk about Fourier Transforms is to avoid talking about phase. It's important, clearly, but it's both less intuitive and less practically meaningful. For a lot of applications, the phase data is just discarded anyway. And if you're in a situation where it matters, you're probably reading more than 3 short paragraphs.
I'd love other thoughts on how to handle the ideas in the last paragraph. I'm not being technical, but am trying to allude to how the complex exponentials can capture more information more conveniently... and honestly waving my hands a lot. Really, I just want to explain why they're there instead of a more recognizable sine or cosine functions.
I've also tried to show the Fourier transform as the sum of a sine and a cosine transform, but that's too much, I think.
Re: The Fourier Transform, explained in one sentence (2014)
#166Ok, my knowledge of the Fourier transform is limited to the discrete version, but I might as well add my take into the mix. :-) I've always thought of the Fourier transform as a series of projections (as in high dimensional dot products). You dot product your signal with a set of sine and cosine waves, which are selected to form an orthogonal basis over the domain of the signal. So it's just a basis transformation. The phase of the wave is captured by the fact that a sine and a cosine of the same frequency, when added together, will always remain a sine function, but with a different phase, depending on the relative amounts of sine and cosine that are added together.
Re: The Fourier Transform, explained in one sentence (2014)
#167Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
> Does "blog post learning" ever really work?
You mean learning by writing a blog post, or learning by reading a blog post? In both cases, the answer is "yes".
> In other words, without having the necessary background at your fingertips it is hard to really grasp the core concepts. That is why, IMHO, reading these blog posts may feel good but will rarely make things really stick.
The problem these posts solve, at least for me, is that despite having the necessary background, some concepts didn't "click" in my mind when I first learned them. I found that if I then read a couple different posts on a specific concept, each with slightly different perspective or way of presenting it, one of them will eventually hit the "sweet spot" and make it "click" in context of all the background I already have (and often cascade into making me understand a few more things in the topical background).
Re: The Fourier Transform, explained in one sentence (2014)
#168Earlier quoted context omitted.
As someone who still doesn't understand the Fourier Transform, this explanation doesn't help, nor does the article's. As a complete noob, your explanation shows off what you know but doesn't help newcomers learn it.
Imagine you have a voice recording. You are looking at it a long squiggly line with no uniformity. Zoom way in. If you go far enough it’ll just look like a curved line. That curved line can be estimated down into a sin wave, or more accurately, a few sin waves that combine to make almost the same wave you have. FFT is a way to take a complex wave and reduce it down to the sin wave components that would all combine to…
Great explanation! I'm finally on the first step of understanding. Now to read more!
Re: The Fourier Transform, explained in one sentence (2014)
#169Honestly, it's not so bad. It's easy to pick any such attempt apart. This is close to my favorite pithy way of explaining it, too, which is to break it down component-wise using the idea of filter banks. It's not a single sentence, but here's what I tend to say: Any signal—like sounds or electrical signals, or even images—can be thought of as having a certain amount of 'energy' at any choice of frequency. This makes…
As someone who still doesn't understand the Fourier Transform, this explanation doesn't help, nor does the article's. As a complete noob, your explanation shows off what you know but doesn't help newcomers learn it.
Apologies, there’s only so much one can do firing explanations into the void. I don’t really mean to show off, but instead to share meanings which I’ve personally had success sharing with others and having them come to better understanding. I can’t hope that it will be what each individual finds most helpful, however. I also have little hope for any “short” resource to accomplish that. I hope you find what you’re looking for.
Re: The Fourier Transform, explained in one sentence (2014)
#170As someone without a lot of math background, the most confusing part of this is k. Is k a number, like 7.45 or whatever? Or something else? Everything else is just normal mathy stuff.
k is the parameter of the function as in the 'x'-axis so instead of saying y=f(x), the formula says y=f(k) You can see in the formula, that it's plugged in as the frequency of the signal the original signal is 'spun-around' with.
Smart. But please give my PCBs back.