Quadrature mirror filter

About: Quadrature mirror filter is a research topic. Over the lifetime, 955 publications have been published within this topic receiving 28900 citations.

Multirate Systems and Filter Banks

Abstract: 1. Introduction 2. Review of Discrete-Time Systems 3. Review of Digital Filters 4. Fundamentals of Multirate Systems 5. Maximally Decimated Filter Banks 6. Paraunitary Perfect Reconstruction Filter Banks 7. Linear Phase Perfect Reconstruction QMF Banks 8. Cosine Modulated Filter Banks 9. Finite Word Length Effects 10. Multirate Filter Bank Theory and Related Topics 11. The Wavelet Transform and Relation to Multirate Filter Banks 12. Multidimensional Multirate Systems 13. Review of Discrete-Time Multi-Input Multi-Output LTI Systems 14. Paraunitary and Lossless Systems Appendices Bibliography Index

Wavelets and filter banks: theory and design

Abstract: The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetries. >

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

Abstract: The basic concepts and building blocks in multirate digital signal processing (DSP), including the digital polyphase representation, are reviewed. Recent progress, as reported by several authors in this area, is discussed. Several applications are described, including 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 narrowband filter coefficients. The M-band quadrature mirror filter (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, is examined in a pseudo-circulant-matrix framework. Unconventional applications of the polyphase concept are discussed. >

A filter family designed for use in quadrature mirror filter banks

Abstract: This paper discusses a family of filters that have been designed for Quadrature Mirror Filter (QMF) Banks. These filters provide a significant improvement over conventional optimal equiripple and window designs when used in QMF banks. The performance criterion for these filters differ from those usually used for filter design in a way which makes the usual filter design techniques difficult to apply. Two filters are actually designed simultaneously, with constraints on the stop band rejection, transition band width, and pass and transition band performance of the QMF filter structure made from those filters. Unlike most filter design problems, the behavior of the transition band is constrained, which places unusual requirements on the design algorithm. The requirement that the overall passband behavior of the QMF bank be constrained (which is a function of the passband and stop band behavior of the filter) also places very unusual requirements on the filter design. The filters were designed using a Hooke and Jeaves optimization routine with a Hanning window prototype. Theoretical results suggest that exactly flat frequency designs cannot be created for filter lengths greater than 2, however, using the discussed procedure, one can obtain QMF banks with as little as ±.0015dB ripple in their frequency response. Due to the nature of QMF filter applications, a small set of filters can be derived which will fit most applications.