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In article <4521@internal.Apple.COM> turk@Apple.COM (Ken "Turk" Turkowski) writes:
>Could anyone explain what a quadrature mirror filter is?
Um, well, I could.  How about a top-level description and
a few pointers to papers?

A QMF (Quadrature Mirror Filter) is a specially designed
type of filter.  It (in its original and simplist form)
splits a signal into two half-bands, and provides for
exact reconstruction, given that the two half-bands are
decimated by two from the original sampling rate.
The Quadrature refers to the fact that the signal
is generated (by decimation) in quadrature, and that
the internal aliasing isn't, i.e. so that  the aliasing
can be cancelled exactly on reconstruction, given
no quantization of the intermediate signals.  The "Mirror"
means that the high pass and low pass filters are exact
mirrors, i.e. one is H(z) and one H(-z).

For an explanatory reference, see Jayant and Noll,
"Digital Coding of Waveforms", Pages 496 to 499.  
For an ICASSP-level discussion, see J D. Johnston,
"A Filter Family Designed for Use in Quadrature Mirror
Filter Banks", Proc. ICASSP 1980, pp291-294.  This paper
also has some coefficients in case you don't want to design
your own.

For a book with more general explanation of the
whole mess, see Crochiere and Rabiner, "Multirate Digital
Processing".

The original paper on the subject (as far as I know)
from the original patent holders, is Esteban and Galand, "Application
of Quadrature Mirror Filters to Split Band Voice Coding
Schemes", proc ASSP 1977, pp 191-195.

Mark Smith and other folks from Ga. Tech have done some
more general approaches with non-FIR models and such,
but I don't know the references.

R. V. Cox has done an 'n' band (n .ge. 2) version,
in ASSP Transactions, Vol ASSP-34 #5, Oct 86, pp 1090-1096,
"The Design of Uniformly and Non-uniformly spaced Pseudo-Quadrature
Mirror Filters". 

These filters have also been used in image processing
(as opposed to audio processing).  A reference that
will lead to more references for image Processing is
ICASSP-89, Safranek and Johnston, <something or other>
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