[music-dsp] Saturation vs Distortion

Dave Gamble signalzerodb at yahoo.co.uk
Mon Mar 3 09:02:00 EST 2003


> Rate changes are linear, but aren't time invariant.
> Think of a signal that
> is zero for all odd-numbered times, and one for all
> even-numbered times.
> Then, if you downsample by two, you get a signal
> that is equal to one for
> all time. If you then shift the input signal by one
> time unit and
> downsample, you get a signal that is always zero. So
> downsampling is
> time-variant.
> 
Yes and no.

The signal you describe is a nyquist sine with
peak-to-peak of 0.5 plus a DC signal with level=1/2.
Obviously, if we downsample, the nyquist sine will
alias.

For this reason, classical downsampling must assume
that the signal has been bandlimited before the
downsampling process.

Downsampling causes aliasing - it does not, however,
add new intermodulatory harmonics.

'Perfect' fourier downsampling (this is my own
opinion) of the form of Stilson+Smith's paper (which
uses sinc interpolation before downsampling) is quite
linear, because the signal has been bandlimited before
downsampling.

Dave.

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