[CST-2] IT&C Nyquist

[Matthew Richards]

> You would not know the amplitude. It could be 0..!

Oops, yes...

> That a signal is band-limited by W means that its frequency spectra lies
> in the range -W < w < W. The highest frequency in the signal (1/(2pi))
> must be (slightly) less than W. Sampling at 2W will then completely
> capture the signal. (if this is right?)

So you mean we need to sample at a rate slightly higher than 1/pi ?  That'd
make sense, and then we would be able to reconstruct the signal.  But the
notes state that the bandlimiting condition is

	F(k) = 0 for |k| > W

So that suggests that the frequency spectrum must be -W <= k <= W, and we're
back where we started.

Since we're basically recording the zero crossings, this begins to look like
Logan's theorem, where we exclude amplitude-modulated versions of signals by
weird side-conditions to do with Hilbert's transform. So is there some
similar side-condition in this case that we're missing?

If we took our samples at x=1, pi+1, 2pi+1, ... (for example) then we
wouldn't have a problem.

Does anyone have any idea?  And there was me thinking I was beginning to
understand this stuff...

Matthew