ashok@atrp.mit.edu (Ashok C. Popat) (09/22/89)
Anybody out there have coefficient values for parallel-structure pseudo-quadrature-mirror filters? The filters needn't be linear-phase, but the reconstructed output should be identical or nearly identical to the input when no intermediate processing is done. I'd be interested in any number of bands greater than two. Thanks in advance. Ashok Chhabedia Popat MIT Rm 36-665 (617) 253-7302
turk@Apple.COM (Ken "Turk" Turkowski) (10/03/89)
Could anyone explain what a quadrature mirror filter is? -- Ken Turkowski @ Apple Computer, Inc., Cupertino, CA Internet: turk@apple.com Applelink: TURKOWSKI1 UUCP: sun!apple!turk
jj) (10/04/89)
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> -- To the Lords of *Mail to jj@alice.att.com or alice!jj Convention *HASA, Atheist Curmudgeon Division 'Twas Claverhouse *Copyright alice!jj 1989, all rights reserved, except Spoke *transmission by USENET and like free facilities granted.