A theory of multirate filter banks

Multirate filter banks produce multiple output signals by filtering and subsampling a single input signal, or conversely, generate a single output by upsampling and interpolating multiple inputs. Two of their main applications are subband coders for speech processing and transmultiplexers for telecommunications. Below, we derive a theoretical framework for the analysis, synthesis, and computational complexity of multirate filter banks. The use of matrix notation leads to basic results derived from properties of linear algebra. Using rank and determinant of filter matrices, it is shown how to obtain aliasing/ crosstalk-free reconstruction, and when perfect reconstruction is possible. The synthesis of filters for filter banks is also explored, three design methods are presented, and finally, the computational complexity is considered.

[1]  Peter Vary,et al.  A short-time spectrum analyzer with polyphase-network and DFT , 1980 .

[2]  M. Vetterli.  Filter banks allowing perfect reconstruction , 1986 .

[3]  Martin Vetterli,et al.  Perfect transmultiplexers , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[4]  Martin Vetterli.  A theory of filter banks , 1986 .

[5]  S. Biyiksiz,et al.  Multirate digital signal processing , 1985, Proceedings of the IEEE.

[6]  Martin Vetterli,et al.  TREE STRUCTURES FOR ORTHOGONAL TRANSFORMS AND APPLICATION TO THE HADAMARD TRANSFORM , 1983 .

[7]  Martin Vetterli,et al.  Pseudo quadrature mirror filters , 1984 .

[8]  H. Nussbaumer.  Polynomial transform implementation of digital filter banks , 1983 .

[9]  G. Wackersreuther,et al.  On the design of filters or ideal QMF and polyphase filter banks , 1985 .

[10]  James L. Flanagan,et al.  Digital coding of speech in sub-bands , 1976, The Bell System Technical Journal.

[11]  Plessis Robinson,et al.  TDM-FDM Transmultiplexer: Digital Polyphase and FFT , 1974 .

[12]  D. Esteban,et al.  Application of quadrature mirror filters to split band voice coding schemes , 1977 .

[13]  M. Vetterli.  Multi-dimensional sub-band coding: Some theory and algorithms , 1984 .

[14]  Thomas Kailath,et al.  Linear Systems , 1980 .

[15]  H. Stone.  Discrete Mathematical Structures and Their Applications , 1973 .

[16]  H. Nussbaumer.  Fast Fourier transform and convolution algorithms , 1981 .

[17]  Peter Vary,et al.  A digital filter bank with polyphase network and FFT hardware: Measurements and applications , 1981 .

[18]  Claude Galand,et al.  Quadrature mirror filters with perfect reconstruction and reduced computational complexity , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  John W. Woods,et al.  Subband coding of images , 1986, IEEE Trans. Acoust. Speech Signal Process..

[20]  Martin Vetterli.  Analysis, synthesis and computational complexity of digital filter banks , 1986 .

[21]  Martin Vetterli,et al.  Splitting a signal into subsampled channels allowing perfect reconstruction , 1985 .

[22]  P. Chu.  Quadrature mirror filter design for an arbitrary number of equal bandwidth channels , 1985, IEEE Trans. Acoust. Speech Signal Process..

[23]  AUe Operationen,et al.  Tree Structures for Orthogonal Transforms and Application to the Hadamard Transform , 1983 .

[24]  James D. Johnston,et al.  A filter family designed for use in quadrature mirror filter banks , 1980, ICASSP.

[25]  C. Galand,et al.  New quadrature mirror filter structures , 1984 .

[26]  P. P. Vaidyanathan,et al.  Theory of uniform DFT, parallel, quadrature mirror filter banks , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  T. Barnwell,et al.  A procedure for designing exact reconstruction filter banks for tree-structured subband coders , 1984, ICASSP.

[28]  Martin Vetterli,et al.  Computationally efficient QMF filter banks , 1984, ICASSP.

[29]  Mark J. T. Smith,et al.  A new filter bank theory for time-frequency representation , 1987, IEEE Trans. Acoust. Speech Signal Process..

[30]  Joseph Rothweiler,et al.  Polyphase quadrature filters-A new subband coding technique , 1983, ICASSP.

[31]  Z. Picel,et al.  Flexible design of computationaly efficient nearly perfect QMF filter banks , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[32]  Mark J. T. Smith,et al.  A unifying framework for analysis/Synthesis systems based on maximally decimated filter banks , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[33]  Mark Jeffrey Troy Smith,et al.  Exact reconstruction analysis/synthesis systems and their application to frequency domain coding , 1984 .

[34]  L. Rabiner,et al.  A digital signal processing approach to interpolation , 1973 .