Abstract
We present a new method for constructing local orthogonal bases, both in continuous and discrete time. All basis functions are obtained from a single prototype window, and there exists a fast algorithm for implementation. The approach is very general and can handle a large variety of cases interesting for applications, such as audio and image coding.
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H. Malvar,Signal Processing with Lapped Transforms, Norwood, MA: Artech House, 1992.
J. Princen, A. Johnson, and A. Bradley, “Subband Transform Coding Using Filter Bank Designs Based on Time Domain Aliasing Cancellation,” inProc. IEEE Int. Conf. Acoust., Speech, and Signal Proc., (Dallas, TX), April 1987, pp. 2161–2164.
C. Herley, J. Kovačević, K. Ramchandran, and M. Vetterli, “Tilings of the Time-Frequency Plane: Construction of Arbitrary Orthogonal Bases and Fast Tiling Algorithms,”IEEE Trans. Signal Proc., Special Issue on Wavelets and Signal Processing, vol. 41, December 1993, pp. 3341–3359.
Y. Meyer,Wavelets: Algorithms and Applications, Philadelphia, PA: SIAM, 1993. Translated and revised by R. D. Ryan.
I. Daubechies,Ten Lectures on Wavelets, Philadelphia, PA: SIAM, 1992.
C. Todd, G. Davidson, M. Davis, L. Fielder, B. Link, and S. Vernon, “AC-3: Flexible Preceptual Coding for Audio Transmission and Storage,” inConvention of the AES, (Amsterdam, Holland), February 1994.
J. Kovačević, D. LeGall, and M. Vetterli, “Image Coding with Windowed Modulated Filter Banks,” inProc. IEEE Int. Conf. Acoust., Speech, and Signal Proc., (Glasgow, UK), May 1989, pp. 1949–1952.
A. Johnson, J. Princen, and M. Chan, “Frequency Scalable Video Coding using the MDCT,” inProc. IEEE Int. Conf. Accoust., Speech, and Signal Proc., (Adelaide, Australia), 1994.
R. Coifman and Y. Meyer, “Remarques sur l'analyse de Fourier à Fenêtre,”C. R. Acad. Sci. Paris, vol. I, 1991, pp. 259–261.
P. Auscher, G. Weiss, and M. V. Wickerhauser, “Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets,” inWavelets: A Tutorial in Theory and Applications (C. Chui, ed.), pp. 237–256, San Diego: Academic Press, 1992.
N. Jacobson,Basic Algebra I, W. H. Freeman, 1985.
X.-G. Xia, and B. W. Suter, “A Family of Two Dimensional Nonseparable Malvar Wavelets,” 1994. Preprint.
R. Bernardini and J. Kovačević, “Local Orthogonal Bases II: Window Design,”Multidim. Syst. and Sign. Proc., Special Issue on Wavelets and multiresolution Signal Processing, July 1996. Invited paper.
J. Serre,Linear Representations of Finite Groups, New York: Springer-Verlag, 1977.
L. Debnath and P. Mikusinski,Introduction to Hilbert Spaces with Applications, New York, NY: Academic Press, 1990.
N. Akhiezer and I. Glazman,Theory of Linear Operators in Hilbert Spaces, vol. 1, Frederick Ungar Publisher, 1966.
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Bernardini, R., Kova<cević, J. Local orthogonal bases I: Construction. Multidim Syst Sign Process 7, 331–369 (1996). https://doi.org/10.1007/BF01826247
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DOI: https://doi.org/10.1007/BF01826247