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Build a sound

Stack pure tones and listen to what you have made. Then check the picture underneath: the transform should find exactly the tones you put in, at exactly the strengths you chose. You supply the right answer, so you can test the tool rather than trust it.

Your tones

Tone 1
Pitch220.0 Hz
Strength0.60
Phase0.00 π
Tone 2
Pitch440.0 Hz
Strength0.30
Phase0.00 π
Tone 3
Pitch660.0 Hz
Strength0.15
Phase0.33 π

The wave you built

What the transform found

20 Hz50 Hz100 Hz200 Hz500 Hz1 kHz2 kHz5 kHz10 kHz20 kHz

Does it come back?

Run the transform, then run it backwards. If it is correct, the signal that comes out is the one that went in — to the last decimal a computer can hold.

PitchYou setFound
220.0 Hz0.6000.000
440.0 Hz0.3000.000
660.0 Hz0.1500.000
Worst deviation
Parseval
0
Peak
1.004

The strengths found come out a shade under the ones you set. That is not an error: a tone whose pitch falls between two bins is shared across both of them, so neither reads its full height. Land a tone exactly on a bin — 187.5 Hz here — and it comes back whole.

Everything else
Window function

Blackman — least leakage, widest peak

Cutting a signal off abruptly invents frequencies that were never in it — leakage. A taper is how that is kept down.

Frequency scale

Linear is what the FFT returns, log matches how pitch is heard, mel matches how hearing spaces it out.