14 May
2021
14 May
'21
1:42 a.m.
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