Fast implementation of wavelet transform for m-band filter banks

Jun Tian; Raymond O. Wells Jr.

doi:10.1117/12.304902

26 March 1998 Fast implementation of wavelet transform for m-band filter banks

Jun Tian, Raymond O. Wells Jr.

Proceedings Volume 3391, Wavelet Applications V; (1998) https://doi.org/10.1117/12.304902
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

Abstract

An orthogonal m-band discrete wavelet transform has an O(m²) complexity. In this paper, we present a fast implementation of such a discrete wavelet transform. In an orthonormal m-band wavelet system, the vanishing moments and orthogonality conditions are imposed on the scaling filter only. Given a scaling filter, one can design the other m-1 wavelet filters. It is well-known that there are infinitely many solutions in such designing procedure. Here we choose one specific type of solutions and implement the corresponding wavelet transform in a scheme which has complexity O(m). Thus for any scaling filter, one can always construct a full orthogonal m-band wavelet matrix with an O(m) discrete wavelet transform.

Citation Download Citation

Jun Tian and Raymond O. Wells Jr. "Fast implementation of wavelet transform for m-band filter banks", Proc. SPIE 3391, Wavelet Applications V, (26 March 1998); https://doi.org/10.1117/12.304902

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