Mon Oct 6 13:30:26 CEST 2008

FFT window design for sinusoidal synthesis

(Mostly note to self.  FIXME: explain this a bit better.)

In 2000 I tried to design windowing functions for spectral synthesis:
synthesizing a sum of sinusoids by constructing a DFT spectrum through
updates of a limited number of frequency components per sinusoid.  I
apporached this as a FIR filter design problem.

However, I came to realize that approaching this as a filter design
problem, focussing only on stationary signals is not sufficient.  The
real problem is about amplitude modulation effects that happen when
mixing subsequent stationary signals, as a result of phase
discontinuities.  The only way to tackle this properly seems to be to
increase the spectral update rate.

It would be interesting to see whether this can be solved in the
DYNWAV model: it already has a variable frequency mechanism (wavetable
playback) which could be used to capture "average" frequency change
without amplitude modulation effects.  However, synthesizing multiple
pitches still gives the same problem.