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How the cochlea computes (2024)

(www.dissonances.blog)
475 points izhak | 1 comments | 30 Oct 25 17:01 UTC | HN request time: 0s | source
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tryauuum ◴[30 Oct 25 17:32 UTC] No.45762674[source]▶
man I need to finally learn what a Fourier transform is
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adzm ◴[30 Oct 25 17:42 UTC] No.45762805[source]▶
the very simplest way to describe it: it is what turns a waveform (amplitude x time) to a spectrogram like on a stereo (amplitude x frequency)
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Chabsff ◴[30 Oct 25 17:46 UTC] No.45762847[source]▶
And phase. People always forget about the phase as if it was purely imaginary.
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JKCalhoun ◴[30 Oct 25 18:35 UTC] No.45763533[source]▶
Ha ha, as I understand it, phase is imaginary in a Fourier transform. Complex numbers are used and the imaginary portion does indeed represent phase.

I have been told that reversing the process — creating a time-based waveform — will not resemble (visually) the original due to this phase loss in the round-tripping. But then our brain never paid phase any mind so it will sound the same to our ears. (Yay, MP3!)

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1. xeonmc ◴[30 Oct 25 19:50 UTC] No.45764495{3}[source]▶
Actually, by the Kramers-Kronig relation you can infer the imaginary part just from the real parts, if given that your time signal is causal. So the phase isn’t actually lost in any way at all, if you assume causality.

Also, pedantic nit: phase would be the imaginary exponent of the spectrum rather than the imaginary part directly, i.e, you take the logarithm of the complex amplitude to get log-magnitude (real) plus phase (imag)