Zero padding and the Shannon information content

On Mar 15, 8:06 pm, "Dave" <Confused.Scient...@gmail.com> wrote:
> Hello all,
>
> I am confused about how zero-filling / windowing a signal alters its
> information content and I'm hoping someone here can help.
>
> I have a continuous signal (time domain) and I Fourier transform it to
> get a band-limited spectrum (frequency domain).  From Shannon &
> Weaver, I can compute the information content of the time domain
> signal from the signal variance and, given the linearity of a DFT, I
> expect the information content of the frequency domain signal is the
> same.
>
> The DFT code that I have has the option of zero-filling/zero-padding
> the original signal as a means of interpolating in the frequency
> domain.  This doesn't change the location/frequency of the peaks in
> the spectrum but does make it easier to accurately locate the maximum
> of each peak.  So, does zero-filling/zero-padding change the
> information content of the signal?

It certainly doesn't add information.  Zero padding in the frequency
domain is identical to sinc interpolation in the time domain.  The
result is just a bunch of weighted averages of the existing
information
content in your original signal vector (minus rounding/quantization
noise).

Windowing might destroy information, especially if any portion
of the window is zero, or small relative to the quantization level.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M