[PD] smallest possible value of a delay-time
Larry Troxler
lt at westnet.com
Tue May 18 18:03:55 CEST 2004
On Monday 17 May 2004 03:18, Mathieu Bouchard wrote:
> 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.
>
I think we must be talking past each other, sorry. The Nyquist theorem states
that a signal bandlimited to some f is _exactly_ recoverable from samples of
the signal at a sample rate greater than 2f, provided that the proper
bandlimited interpolation is used. There is no issue with "a limitied number
of allowable phases". So no, the Nyquist requirement is not for a frequency
to be representable at all, it's for a non-time-limited frequency to be
represented exactly, phase and all.
Larry Troxler
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