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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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eric-burel ◴[05 Sep 25 11:45 UTC] No.45137452[source]▶
What always bothered me when trying to "feel" Fourier transforms is that to compute the oscillations, you need to wait some time. Mathematically, the transformation includes computing integrals. So it's tricky to understand how you compute the Fourier decomposition for a stream. Illustrations always show the whole signal over time but in real life you get the signal progressively. I'd be eager to read more on this.
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1. thyristan ◴[05 Sep 25 12:06 UTC] No.45137594[source]▶
For a stream, you use a sliding window to compute the FFT. The size of the window of course limits the lowest frequency range that you can 'see', same for the highest frequency through the time quantization that digital data usually has. So there will be an upper and lower frequency limit, beyond those limits the results are meaningless.

And the window of course creates a latency, which is sometimes relevant for realtime audio filtering by FFT.