Conjointly well localized modulated lapped orthogonal transforms

This paper proposes the particle swarm optimization method to determine conjointly time-frequency well localized filters that constitute a multi-channel perfect reconstruction filterbank. The time-frequency measure to determine optimality is the product of a filter's time and frequency variances. The optimization process involving multiple free parameters is computationally expensive. Optimization methods require long computation time that increases exponentially with the number of free parameters to achieve good results. The particle swarm optimization provides an effective and efficient method to determine optimality. We propose the use of the particle swarm optimization method to determine optimal complex modulated lapped transform filters.

[1]  Scott T. Acton,et al.  Properties of the magnitude terms of orthogonal scaling functions , 2010, Digit. Signal Process..

[2]  Chang Wen Chen,et al.  Visual Information Representation, Communication, and Image Processing , 1999 .

[3]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[4]  C. Frank,et al.  An Uncertain Life: Uncertainty: The Life and Science of Werner Heisenberg , 1994 .

[5]  Martin Vetterli,et al.  Perfect reconstruction FIR filter banks: some properties and factorizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[6]  Mark J. T. Smith,et al.  Exact reconstruction techniques for tree-structured subband coders , 1986, IEEE Trans. Acoust. Speech Signal Process..

[7]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[8]  J. Daugman Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[9]  Victor E. DeBrunner,et al.  The optimal solutions to the continuous and discrete-time versions of the Hirschman uncertainty principle , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[10]  P. P. Vaidyanathan Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands , 1985 .

[11]  Milos Doroslovacki,et al.  Discrete-time signals and uncertainty relations involving ordinary second moments in time and frequency , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[12]  Victor E. DeBrunner,et al.  Resolution in time-frequency , 1999, IEEE Trans. Signal Process..

[13]  Mark J. T. Smith,et al.  Analysis/synthesis techniques for subband image coding , 1990, IEEE Trans. Acoust. Speech Signal Process..

[14]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[15]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[16]  Mark J. T. Smith,et al.  The time domain analysis and design of exactly reconstructing FIR analysis/synthesis filter banks , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[17]  Thomas P. Barnwell,et al.  A time domain view of filter banks and wavelets , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[18]  Xiaojun Wu,et al.  Quantum-Behaved Particle Swarm Optimization: Analysis of Individual Particle Behavior and Parameter Selection , 2012, Evolutionary Computation.

[19]  Henrique S. Malvar Lapped transforms for efficient transform/subband coding , 1990, IEEE Trans. Acoust. Speech Signal Process..

[20]  Victor E. DeBrunner,et al.  A novel translation and modulation invariant discrete-discrete uncertainty measure , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[21]  D. Donoho,et al.  Uncertainty principles and signal recovery , 1989 .

[22]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

[23]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[24]  Alan C. Bovik,et al.  Multidimensional quasi-eigenfunction approximations and multicomponent AM-FM models , 2000, IEEE Trans. Image Process..

[25]  P. P. Vaidyanathan,et al.  Theory and design of optimum FIR compaction filters , 1998, IEEE Trans. Signal Process..