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What Is the Fourier Transform?

(www.quantamagazine.org)
474 points rbanffy | 1 comments | 04 Sep 25 22:11 UTC | HN request time: 0s | source
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trgn ◴[05 Sep 25 16:14 UTC] No.45140227[source]▶
Can somebody eli5, im an amateur. How does the transform know the frequencies of the output. Do you have to specify a number n, and then it decomposes it into n frequencies. Or do you give it a list of frequencies, and then it decomposes the coefficient or amplitude or something for each?

I guess what i want to know, in the examples it always shows like 3 or 4 constituents frequencies as output, but why not hundreds or a million? Is that decided upfront /paramtetizable?

The article isn't helpful, it just says something like "all possible frequencies".

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1. slickytail ◴[05 Sep 25 16:37 UTC] No.45140548[source]▶
In a discrete Fourier transform, the number of frequencies you get out is the number of datapoints you have as input. This is because any frequencies higher than that are impossible to know (ie, they are above the sampling frequency).

But in the continuous Fourier transform, the output you get is a continuous function that's defined on the entire real line.