Make the transform a Fourier transform

[ibrahimweng]

listen.ts is how the app reads sounds out of a recording — find where they are, then say whether two are the same kind of thing. Underneath all of it is a Fourier transform, and it was not one.

What was wrong

The angle it multiplies by was turned once per block instead of once per butterfly:

for (let k = 0; k < len / 2; k++) { ...butterflies using cr, ci... }
const nr = cr * wr - ci * wi;   // ← outside the loop

So every butterfly in a block used the angle it started at, which is no angle at all. What that computes is a Walsh–Hadamard transform.

A five-cycle cosine, which belongs in bin 5 and nowhere else:

naive DFT non-zero bins: 5
this fft non-zero bins:  1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31
                         peak at 15

Only one kind of test could find it

Every test that compares one fingerprint against another passes on a transform that is merely consistent — and this one was. It scrambled every spectrum the same way, so two takes of a sound still matched and nothing above it ever complained. What was lost was every comparison between sounds that are not the same, which is the whole of what this file does.

It took a naive DFT, written straight from the definition and slow enough that nobody would ship it. After the fix, the two agree to 4.6e-13.

The comment above it says why this matters

The four pages under tools/ have the same transform with the line in the right place. This copy is the one that moved, and its own comment reads:

moved here so that the app and the pages that measure it cannot come to disagree about what a sound looks like

They had come to disagree.

Thirteen tests

The DFT comparison, a tone landing in its own bin at five frequencies, silence staying silent, a constant living entirely in bin zero, and what the fingerprint is actually for — taking out what a set of sounds have in common pushes two of the same kind apart, 0.95 → 0.45.

Three of those tests were mine and wrong first, which is worth saying: mono doesn't take the centre out, ordinary averages the logs rather than the prints, and a quieter take of a sound isn't identical to it (half a print is how loud each slice was) — so that one now asks whether it's nearer to itself than to something else, rather than asking for a number I picked.

333 unit tests (was 320), 88 browser tests, build clean.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Ux1kydvUkLRoMbHp82ofDi

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Generated by Claude Code

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