[alma-config]Re: Nyquist and more

[John Conway]

Hi,

 I include the protomemo I wrote a few weeks
ago and sent to Frederik on the subject 
of irregular sampling. I took a Fourier
domain approach - I later found as Dave 
notes that the same problem was dealt with 
already by Bracewell in his book, in terms 
of the required convolving functions 
in the signal domain which is much simpler,  
however Bracewell he does not calculate an 
expression for  the increase in noise as a function 
of the displacement from irregularity 
for an interleaved sequence- this calcualtion 
shows that the increase in noise is 
not as large for small displacemnets  from regularity 
as  is sometimes claimed.  In between teaching 
and writing long emails I havn't had chance to 
check the paper by Linden quoted by Bracewell.

I can't be sure there are no typos in the
memo since I have had had little time to check.

   John


On Mon, 8 Oct 2001, David Woody wrote:

> Some information on Nyquist sampling.
> 
> There is a generalization of the Nyquist
> theorem that we all know and love that says
> that all you really need is that the average
> sampling over the time interval (or UV-plane)
> be consistent with the band limited Nyquist
> sampling theorem.  This is briefly discussed
> in Bracewell "Fourier Transform and its
> applications" 3rd edition, 2000, pp.232-235
> and an article by D. A. Linden, "A discussion
> of sampling theorems", Proc. IRE vol. 47, 
> p. 1219, 1959.
> 
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