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The Fourier Transform, explained in one sentence (2014)

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Re: The Fourier Transform, explained in one sentence (2014)

#71

Post by avip »

prof-dr-ir wrote: post #69

Does "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…

I think you’re confusing proving with understanding. The two are almost orthogonal.

Re: The Fourier Transform, explained in one sentence (2014)

#73

Post by posix86 »

avip wrote: post #71
prof-dr-ir wrote: post #69

Does "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…

I think you’re confusing proving with understanding . The two are almost orthogonal.

Disagree. If you truly understand something, you must have prooven it to yourself, everything is just a mental help ("donkey bridge" in german) that allows you to remember the statement better - weather it's right or not, you can only know once you've prooven it; and before you did that, it can often happen that your intuition on what's right is actually wrong.

Re: The Fourier Transform, explained in one sentence (2014)

#74

Post by posix86 »

wkjagt wrote: post #37
sebzim4500 wrote: post #14

This reminds me of an old joke in the Haskell community, where people who struggled to understand Monads would finally get it after a while, and would assume that whatever the last sentence they heard was the only necessary one for the explanation.

I’ve understood monads multiple times in my life, but each time that understanding was so fragile that it crumbled when I tried explaining to someone else. I’m currently in a phase where I don’t understand them.

This is 100% how I feel too haha. And everytime I loose the feeling of understanding them, I question if I understood them before.

Re: The Fourier Transform, explained in one sentence (2014)

#75

Post by trenchgun »

TedDoesntTalk wrote: post #60
johnday wrote: post #42

Earlier quoted context omitted.

A monad is a computational context, where the nature of that context is determined by two things: the shape of the data structure corresponding to it, and the definition of (>>=) which handles sequencing of two computations in that context. Anything more specific than that should be handled case-by-case until you build an intuition for how any given monad will behave.

Is computational context another way of saying scope?

Not exactly.

Computational context in this sense is like, is this computation of the type that can either fail or succeed? (Maybe monad). Or is this computation of the type that can produce multiple values of the same type? (List monad). Or maybe this computation can produce value of one type or another (Either monad). Or a computation that can interacti with inputs and outputs (IO monad).

So these are computations in differend kinds of computational "worlds" in a sense, with different rules on how such a computation in this context composes.

Re: The Fourier Transform, explained in one sentence (2014)

#76

Post by osigurdson »

prof-dr-ir wrote: post #69

Does "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…

I think a lot of people have heard of the Fourier transform and kind of understand how any signal can be represented by a superposition of sine waves. Attempting to improve the intuition of how the algorithm works isn't a bad thing. The casual reader isn't going to invest the time to learn the pre-requisites so the alternative is nothing at all.

Re: The Fourier Transform, explained in one sentence (2014)

#77

Post by glitchc »

tel wrote: post #16

Honestly, 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…

That's better than the blog post actually (ECE background here).

Re: The Fourier Transform, explained in one sentence (2014)

#79

Post by adlpz »

posix86 wrote: post #73
avip wrote: post #71

Earlier quoted context omitted.

I think you’re confusing proving with understanding . The two are almost orthogonal.

Disagree. If you truly understand something, you must have prooven it to yourself, everything is just a mental help ("donkey bridge" in german) that allows you to remember the statement better - weather it's right or not, you can only know once you've prooven it; and before you did that, it can often happen that your intuition on what's right is actually wrong.

That makes no sense to me. Or maybe your definition of "understand" is completely unrelated to mine.

Under your thesis one cannot "understand" anything physical (as in physics, chemistry, etc) as the underlying cannot be "proven", at all, by definition.

Re: The Fourier Transform, explained in one sentence (2014)

#80

Post by blippage »

Here's my explanation: think of linear regression. Now ask yourself, what if I applied the idea of correlation/regression to a sine wave. An (audio) signal can be broken down into an addition of sine waves having different frequencies and phases. That, conceptually, is what we're trying to do with the Fourier Transform. What frequencies is the sound wave composed of, and of what amplitude. Phase angle is a consideration, but we are less interested in that.

OK, that's a paragraph instead of a sentence, but it does motivate the whole raison d'etre of "why would I care anyway?"

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