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Re: [Discuss-gnuradio] *much* faster filtering --- plus vhf mountaintopp
Re: [Discuss-gnuradio] *much* faster filtering --- plus vhf mountaintopping
Wed, 11 May 2005 12:50:08 -0400
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James Cooley wrote:
there's a way to come up with a compression scheme that's tailored to
the sort of sample data we see...
A topic for a dissertation if ever there was one :-)
In the general case, you're going to have to work hard to
beat Ziv-Lempel. You might improve the performance somewhat
by tweaking the parameters, but probably not a lot.
The problem is that, as we know, in the general case,
compressibility is basically the reciprocal of entropy.
Ziv-Lempel depends on conditional entropy being lower, and
thus compressibility being higher, through markovity.
For most human-generated signals, the influence of the past
(the markovity) decays exponentially towards the past. For
general signals, the decay is very rapid, so there's going
to be a lot of slop at the boundaries of the underlying
markov model. There's also a theorem in there somewhere (due
to Rissanen, I think) that says there's a limit on how much
slop you can trim by tuning the adaptation.
Where you might win is by picking different compression
algorithms depending on the signals. For example, for
voice-bandwidth channels, you might gain a lot from first
converting to mu-law and then gzipping. And so on. For wide,
densely-packed signals, you can probably forget it. The fact
that they're densely packed means they're already high-entropy.