Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

P.P. Vaidyanathan
1990 Proceedings of the IEEE  
Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the
more » ... concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed. Perfect-reconstruction two-channel QMF banks are introduced by blending the polyphase concept with the classical network-theoretic concept of losslessness. The relation between M-band QMF banks and two other related topics (block filtering and periodically time-varying systems) is reviewed in section VII, based on an algebraic structure called the pseudo-circulant matrix. In section VIII, M-band QMF banks are discussed in greater detail, and techniques for elimination of aliasing, amplitude, and phase distortions are reviewed. Section IX discusses unconventional applications, and Section X discusses some extensions of multirate ideas to cases of multidimensional signals. The paper concludes with a discussion of open problems in multirate DSP.
doi:10.1109/5.52200 fatcat:257nblzgxfaodhm4yeblla3n5y