Re: Convolution, channel-selectiveness of effects and spectrograms

Hello Sergei,


thanks for your clarification!

 > > [Thomas does not quite understand the implications of the
 > >  cancellation]
 > The issue, as already pointed out, is spectral resolution. I.e. when
 > two adjacent DFT bins frequencies become the same, instead of having
 > two SEPARATE bins (maybe with some magnitude error) we have a
 > DUPLICATED bin.

Okay, that sounds plausible.

 > Regarding the "whether it invalidates the complete transformation or
 > only part of it" in DFT by its nature (see the link to FFTW
 > documentation) every point in frequency domain depends on every
 > point in time domain and vice versa. But the detrimental effect is
 > most pronounced the peaks/dips of 'cos' and 'sin' components.

I am quite aware of the juggling around of factors in the FFT
algorithm, but I have no good mental model of the effects when some
coefficients are bad.  My gut feeling is that the transformation
results are collectively off somehow, but I cannot quantify how far.

 > Regarding "cos(1/n)" in your estimates - I think it should rather be
 > cos(2 * pi / N).

That's correct, sorry for the lapse.  So there is a factor of six
missing. The correct analysis is:
     cos(0) - cos(2*pi/n) = 1 - cos(2*pi/n) < m
     ==> n > 2*pi/arccos(1 - m)

I have to still think whether the maximum acceptable distance is
2^(-24) (resp. 2^(-53) for double) or one magnitude less, but at
least we are in the ballpark described by you.


	Best regards,

		Thomas