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Date: Sun, 4 Nov 2012 15:34:16 -0800 (PST)
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Subject: Re: Relationship between a functions derivitives and BW?
From: Robert Adams <robert.ad...@analog.com>
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I'm quite sure that you can exceed the value of 2piAF for short periods of =
time if you consider non-sinuousodal inputs that are custom designed to pro=
duce the highest peak derivative.=20

The original poster spoke of a low pass random process, so that means we mu=
st think of a discrete-time random source driving a low pass filter with a =
certain impulse response. This filter defines what we mean by "band limited=
" in this case, and therefore we have the usual trade off between the filte=
r length and the stopband attenuation and the transition bandwidth, but we =
can approach the ideal by assuming this filter is very long. In that case t=
here is a specific input sequence that, at a single sample index, will prod=
uce the highest output possible given that the input is constrained to live=
 between -1 and 1.  This maximum output is far above the +1/-1 limit. Likew=
ise there is a way to construct an input sequence that will produce the lar=
gest pairwise delta, and this value is far above the 2piAF maximum that you=
 would get with a sine-wave input.=20

I guess I am somewhat sensitive to this issue because I once designed a chi=
p that implemented a filter, and I allocated a certain number of bits to th=
e datapath