FFT

[Tom May]

Rene Schmitz <uzs159 at uni-bonn.de> writes:

> >- Take the phase values for one of the waveforms (i.e. the phase value
> >in each FFT bin) and interpolate the magnitude values for each bin to
> >the desired point in between.
> 
> >- Do the same, but interpolate the phase values, too.
> 
> But FFT is a transformation which obeys FFT(x+y) = FFT(x)+FFT(y)
> and also linear FFT(c*x)=c*FFT(x). Where x,y element of C^n, c = const.
> This would mean that all you'd get is a expensive way of mixing.

Right.  But, consider the case where you are transforming from sin(t)
to -sin(t).  You can do it the mixing way like you describe (mixing
either the time or frequency domain values), in which the amplitude
will decrease, cross through zero, and increase on the negative side.
Or you could interpolate the magnitude and phase of the frequency
response separately, in which case you would maintain a constant
amplitude of 1 but the phase would shift from zero to 180 degrees.

fTom.