Recursive Orthonormal Wavelet Bases with Vanishing Moments

Xi ZHANG  Toshinori YOSHIKAWA  Hiroshi IWAKURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.8   pp.1472-1477
Publication Date: 1997/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
orthonormal wavelet,  paraunitary filter bank,  IIR filter,  eigenvalue problem,  

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This paper presents a new method for constructing orthonormal wavelet bases with vanishing moments based on general IIR filters. It is well-known that orthonormal wavelet bases can be generated by paraunitary filter banks. Then, synthesis of orthonormal wavelet bases can be reduced to design of paraunitary filter banks. From the orthonormality and regularity of wavelets, we derive some constraints to IIR filter banks, and investigate relations between the constrained filter coefficients and its zeros and poles. According to these relations, we can apply Remez exchange algorithm in stopband directly, and formulate the design problem in the form of an eigenvalue problem. Therefore, a set of filter coefficients can be easily computed by solving the eigenvalue problem, and the optimal filter coefficients with an equiripple response can be obtained after applying an iteration procedure. The proposed procedure is computationally efficient, and the number of vanishing moments can be arbitrarily specified.