On Thu, May 13, 2021 at 09:27:57PM +0200, Jeanette C. wrote: > May 13 2021, Fons Adriaensen has written: > ... > > FFT theory will provide > > a solution. If you want to think about it, I can give you two hints: > > > > * It's related to the sin() vs. cos() thing mentioned earlier. > > * In this particular case there's an extra twist to it - think > > of shifting a cyclic waveform in time by half a sample.
> Could it be as simple, as bluntly put: forget about the phase, only use > the amplitude/overall power of any harmonic from an FFT and reconstrcut > the signal from all sines at 0 phase? Absolutely right ! Except that for the FFT, sin() means the phase is +/- 90 degrees, remember than sin() components turn up in the imaginary part, with the real part zero. Now imagine the 128 samples generated by T [i] = sin (h * i * 2 * pi / 128), for i = 0...127, and fixed h (h = harmonic number, 0...64). For each h, and also for any waveform which is a sum of these sine waves, we will have T [64+i] = -T [64-i] or equivalently T [128-i] = -T [i] That means we have anti-symmetry w.r.t. samples 0 and 64. Now consider again the sysex format: to make up a cycle of 128 samples the first 64 samples are repeated in reverse order and negated. Now ask yourself: where is the symmetry point in that case ? Ciao, -- FA _______________________________________________ Linux-audio-dev mailing list Linux-audio-dev@lists.linuxaudio.org https://lists.linuxaudio.org/listinfo/linux-audio-dev
