[PLUG] Digital Signal Processing?

Keith Lofstrom keithl at kl-ic.com
Thu May 26 15:38:58 UTC 2005


On Wed, May 25, 2005 at 03:26:23PM -0700, Russell Senior wrote:
> 
> I am trying to figure out how to apply a Hamming (or Kaiser or various
> alternative) window to a time-domain sample prior to an FFT in order
> to more accurate characterize amplitude of an embedded signal.  I
> don't actually care _that much_ about the frequency, but I care a lot
> about the amplitude.  The literature I've found so far is a few steps
> over my head at the moment and I don't have the time to climb that
> twisting staircase of understanding now.  Can anyone point me at a
> practical treatment of how to apply these windows to data?

Lots out there.  Very simply, windowing is merely a matter of weighting
the input data before applying the FFT to it, to minimize some of the
artifacts that result from the limited sample size.  

For example, if the sample domain ranges from zero to 2pi, then raised
cosine weighting would multiply each data point in your data window by
( 1-cos(X) ), which doubles the weight of the middle points and makes
the endpoints disappear.  This flattens out the apparent frequency
response, which is important for correct conclusions in some analyses.

The different windows have different functions, a bit harder to describe
but still easy to compute, which result in different artifacts in the
result.   Whatever you do to restrict data, however, will result in
some distortion in the result.  The choice of windows should be done
with an eye towards what kinds of decisions you must make using those
results.

Keith

-- 
Keith Lofstrom          keithl at keithl.com         Voice (503)-520-1993
KLIC --- Keith Lofstrom Integrated Circuits --- "Your Ideas in Silicon"
Design Contracting in Bipolar and CMOS - Analog, Digital, and Scan ICs



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