Polyphase Quadrature Filters

Background

While working for RCA I started looking at the problem of filtering a digital audio signal into multiple frequency bands, in such a way that

the bands can be recombined to nearly exactly reproduce the original signal.

The total number of samples stays the same. For example, filtering an 8000 samples/second stream into 8 streams at 1000 samples/second each. Previously, quadrature mirror filters (QMF) had been used to split a band into two equal bands with half the sampling rate. Trees of QMF's could therefore be used to split a signal into more than 2 bands.

Also, techniques had been developed to do multiband filtering using frequency transforms (FFT or DCT). However, these techniques required an increase in the total number of samples.

The key contribution of this paper is the development of a computationally efficient way to perform multiband filtering using a single prototype filter and a Discrete Cosine Transform (DCT). By properly phasing the different bands, it is possible to cancel the resulting aliasing, and recover the original signal.

The original application was subband coding of speech signals. A similarity has been noted between this technique and the filter bank used in the MPEG-2 Audio Codec III (the so-called mp3 files). For example, in "A Tutorial on MPEG/Audio Compression" by Davis Pan, he states:

The ISO MPEG audio standard describes a procedure for computing the analysis polyphase filter outputs that is very similar to a method described by Rothweiler

A list of citations of this paper is available at http://citeseer.ist.psu.edu/context/609944/0

For my paper I referred to this type of filter bank as a Polyphase Quadrature filter bank, combining the names of the two-band and multiband filter structures. Today, it is more commonly referred to as a pseudo-QMF (PQMF) filter bank, which is distinct from the perfect-reconstruction (PR) filterbanks that were later developed by other researchers. As the name implies, PR filterbanks can combine the subbands to exactly recover the input signal, while the PQMF approach only approximately recovers it.

However, with reasonable filters, the pseudo-QMF approach can achieve reconstruction with 60 dB or more of attenuation of the error components, so they are quite adequate for most practical purposes.

Other References

Some folks have created a Wikipedia page on the subject of Polyphase Quadrature Filters.

Paper

Copyright information.
The publisher, IEEE, requires the following copyright notice to be posted. For more information, check the IEEE policy (6.2.10). (Note, this link was correct when I originally created this page. I'm looking for a better direct link to the current policy.)

"© 1983 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."

To view to download the paper: icassp83_27-2.pdf (327337 bytes)
This PDF file is a scanned image of the published paper.
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RCA also filed a patent: "System for digital multiband filtering", United States Patent 4,691,292, issued September 1, 1987, and all rights were assigned to them. Trivia: After I left RCA it was purchased by GE, which sold that division to Martin Marietta, which merged with Lockheed to become Lockheed-Martin, which spun of my old group as part of what became L-3 Communications. After I became aware of the Pan article I attempted to find out who owned the rights to the patent and whether they were making any money from it. I was not able to find the owner, so I don't know if anyone benefited.