Orthogonal multiwavelets with optimum time-frequency resolution

A procedure to design orthogonal multiwavelets with good time-frequency resolution is introduced. Formulas to compute the time-durations and the frequency-bandwidths of scaling functions and multiwavelets are obtained. Parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric/antisymmetric scaling functions and multiwavelets supported in [O,N] are presented for N=2,...,6. Orthogonal multiwavelets with optimum time-frequency resolution are constructed, and some optimal multifilter banks are provided.

[1]  O. Rioul,et al.  Wavelets and signal processing , 1991, IEEE Signal Processing Magazine.

[2]  G. Plonka.  Approximation order provided by refinable function vectors , 1997 .

[3]  Qingtang Jiang.  Multivariate matrix refinable functions with arbitrary matrix dilation , 1999 .

[4]  G. Strang,et al.  Approximation by translates of refinable functions , 1996 .

[5]  A. Papoulis.  Signal Analysis , 1977 .

[6]  S. L. Lee,et al.  Wavelets in wandering subspaces , 1993 .

[7]  Charles A. Micchelli,et al.  Regularity of multiwavelets , 1997, Adv. Comput. Math..

[8]  W. Lawton.  Necessary and sufficient conditions for constructing orthonormal wavelet bases , 1991 .

[9]  Hui Xie,et al.  Design of orthonormal wavelets with better time-frequency resolution , 1994, Defense, Security, and Sensing.

[10]  Dennis Gabor,et al.  Theory of communication , 1946 .

[11]  Zuowei Shen.  Refinable function vectors , 1998 .

[12]  D. Hardin,et al.  Fractal Functions and Wavelet Expansions Based on Several Scaling Functions , 1994 .

[13]  George C. Donovan,et al.  Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets , 1996 .

[14]  Ali N. Akansu,et al.  Time-frequency localization in transforms, subbands, and wavelets: a critical review , 1993 .

[15]  Zuowei Shen,et al.  An algorithm for matrix extension and wavelet construction , 1996, Math. Comput..

[16]  S. L. Lee,et al.  WAVELETS OF MULTIPLICITY r , 1994 .

[17]  Hui Xie,et al.  More results on orthogonal wavelets with optimum time-frequency resolution , 1995, Defense, Security, and Sensing.

[18]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[19]  L. Villemoes.  Energy moments in time and frequency for two-scale difference equation solutions and wavelets , 1992 .

[20]  R. DeVore,et al.  The Structure of Finitely Generated Shift-Invariant Spaces in , 1992 .

[21]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[22]  George C. Donovan,et al.  Construction of Orthogonal Wavelets Using Fractal Interpolation Functions , 1996 .

[23]  Gilbert Strang,et al.  Short wavelets and matrix dilation equations , 1995, IEEE Trans. Signal Process..

[24]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[25]  Zuowei Shen,et al.  Multiresolution and wavelets , 1994, Proceedings of the Edinburgh Mathematical Society.

[26]  Martin Vetterli,et al.  Balanced multiwavelets , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[28]  C. Chui,et al.  A study of orthonormal multi-wavelets , 1996 .

[29]  I. Daubechies,et al.  Regularity of refinable function vectors , 1997 .

[30]  Qingtang Jiang,et al.  On Existence and Weak Stability of Matrix Refinable Functions , 1999 .

[31]  Qingtang Jiang.  On the regularity of matrix refinable functions , 1998 .

[32]  Wayne Lawton,et al.  Multiresolution properties of the wavelet Galerkin operator , 1991 .

[33]  C. Dorize,et al.  Optimizing time-frequency resolution of orthonormal wavelets , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.