[PD] smallest possible value of a delay-time

Mathieu Bouchard matju at sympatico.ca
Mon May 17 09:18:13 CEST 2004

On Sun, 16 May 2004, Larry Troxler wrote:

> > Suppose you have a signal at exactly the Nyquist frequency and
> > RMS=sqrt(2). Then its data is like +1,-1,+1,-1,...
> Isn't that a pathological case though? I thought the Nyquist
> requirement was SR > Fmax, not SR >= Fmax.

The Nyquist requirement is for a given frequency to be not representable
at all. What I mean is that even before going beyond Nyquist, you hit
other problems, such that, even though a frequency is still representable,
you have a limited number of allowable phases for it, and that trying to
synthesize the "wrong" phases may cause the output to be quiet, silent, or
full of interference patterns.

> Yes, namely what you are attempting to prove.

That, for even for representable frequencies, one may be unable to shift
phase in small enough increments for the delay to be less than one sample.
That is, without completely borking the signal or rounding down to no
effect at all.

For lower frequencies, that problem may be less apparent, and maybe it
would be possible to do it. If I were to do it in practice, I'd use a
[fft~] and then do appropriate phase shifts and see experimentally whether
it works, but then, I don't know why I'd ever use such small delays... Any
idea why subsample delays would be useful?

Mathieu Bouchard                       http://artengine.ca/matju

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