Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation

Wang wei-wei; Shui Peng-lang

Volume 27 Issue 11

Nov. 2005

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2005 > 27(11): 1765-1769

Wang wei-wei, Shui Peng-lang. Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation[J]. Journal of Electronics & Information Technology, 2005, 27(11): 1765-1769.

Citation:

Wang wei-wei, Shui Peng-lang. Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation[J]. Journal of Electronics & Information Technology, 2005, 27(11): 1765-1769.

Wang wei-wei, Shui Peng-lang. Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation[J]. Journal of Electronics & Information Technology, 2005, 27(11): 1765-1769.

Citation:

Wang wei-wei, Shui Peng-lang. Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation[J]. Journal of Electronics & Information Technology, 2005, 27(11): 1765-1769.

PDF( 221 KB)

Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation

Received Date: 2004-04-26
Rev Recd Date: 2004-12-16
Publish Date: 2005-11-19

Abstract

Abstract

This paper presents a novel method to design prefilters starting from analysis scaling functions and utilizing the algebraic polynomial interpolation. In the case of uniform sampling, the obtained prefilters are time-invariant and its coefficients are linear combinations of the moments of the analysis scaling function. Its approximate order is dependent on the support length of analysis scaling function rather than its degree of regularity. This method provides two outstanding advantages: the prefilters can be designed with higher approximate orders than the existing prefilters, e.g., the special prefilters from the values at integer points of the synthesis scaling function and the prefilters from prescaling function method; moreover, the method is easy to be extended to the case of nonuniform sampling, in which the prefilters are time-variant and their approximate order is dependent on the support length of analysis scaling function as well as the distribution of sample points.

FullText(HTML)

References(1)

References

Strang G. Wavelets and dilation equations: A brief introduction. SIAM Rev., 1989, 31: 613-627.[2]Sweldens W, Piessens R. Quadrature formulae and asymptotic error expansions for wavelet approximation of smooth functions[J].SIAM J. Numer. Anal.1994, 31(4):1240-1264[3]Unser M. Approximation power of biorthogonal waveletexpansio-[4]ns. IEEE Trans. on Signal Processing, 1996, 44(3): 519-527.[5]Zhang J K. 小波级数变换的初始化及M-带插值小波理论研究. [博士论文], 西安: 西安电子科技大学, 1999.[6]Zhang J K, Bao Z. Initialization of orthogonal discrete wavelet transforms[J].IEEE Trans.on Signal Processing.2000, 48(5):1474-1477[7]Abry P, Flandrin P. On the initialization of the discrete wavelet transform algorithm[J].IEEE Signal Processing Lett.1994, 1(2):32-34[8]Xia X G, Kuo C C J, Zhang Z. Wavelet coefficient computation with optimal prefiltering[J].IEEE Trans.on Signal Processing.1994, 42(8):2191-2197[9]Steffen P, Heller P N, Gopinath R A. Theory of regular M-band wavelet bases[J].IEEE Trans. onSignal Processing.1993, 41(12):3497-3511[10]Burden R L, Faires J D. Numerical Analysis. Brooks/Cole, Thomson Learning, Inc., 1998: 107-166.[11]Cohen A, Daubechies I, Feauveau J C. Biorthogonal bases of compactly supported wavelets[J].Commun. Pure Appl. Math.1992, 45(5):485-560[12]Sweldens W. The lifting scheme: a construction of second generation wavelets[J].SIAM J. Math. Anal.1997, 29(2):511-546

Relative Articles

Supplements(0)

Cited By

Proportional views