Re: Oversampling and the FFT

JohnReno wrote:
Hello,
I was recently working with a DSP engineer who was making an argument to
me that if I didn't oversample (above Nyquist) that I would be "losing
information," and I still fail to understand exactly what information I
would be losing. The context of our particular application, is that we are
dwelling on a signal for a fixed period of time (a design constraint), but
we can sample at whatever rate we want. In my mind, higher sample rates
losely translate into more expensive A/Ds and higher processing overhead.
I suggested we sample just above Nyquist and perform our 1024 point FFT.
He said he would prefer to sample at 3x Nyquist. Okay, more samples are
better, I guess, but I don't know how they give more information other
than adding length to the FFT. The dwell time sets the "bin width" and
increasing N, by decreasing Ts to support a fixed dwell, does nothing more
than increase the number of bins in the FFT. The window function used
dictates, to some degree the energy split or "straddling loss" between
bins if the frequency of the sampled signal fails to fall directly on a
FFT bin, but I can pick whatever window I want without regard to the
sample rate. We are doing a complex FFT, and phase information is
important in this particular application, but I fail to see that there is
any loss of phase info, regardless of the window function or sample rate.
I have been working with DFTs/FFTs for a number of years, althought I am an
analyst, not a DSP Engineer. Could someone tell me what fundamental
concept I am missing.

When dealing with perfect samples from a perfectly bandlimited
signal, then sampling above Nyquist is invertable, which means
that no information is lost. However in the real world, there
are effects due to the finite slope of any bandlimiting filters,
which can either lose information from the signal of interest
by pass-band ripple, and/or add alias information from having a
non-zero stop-band. Also the phase of a sharp filter may change
more rapidly near the transition which may amplify any phase noise.
A higher sampling rate not only allows a flatter filter both in
magnitude and phase response, but even if the filter isn't changed,
contaminates signal data with less of any alias noise, due to
folding less of the stop band into the samples. The more noise
you add to a set of samples, the less information it can carry.

Also, but I'm not sure of this, quantization errors (either in
the sampling or inside the FFT) might have a greater effect on
signals near the Nyquist frequency of a given sampling rate than
on those farther below it. Again, adding error reduces information
carrying capacity.


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

.

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