Multirate systems with shortest spline-wavelet filters

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• 作者：Charles K. Chui^a ; ^{ckchui@stanford.edu" class="auth_mail" title="E-mail the corresponding author} ; Johan de Villiers^b ; ^c ; ^{jmdv@sun.ac.za" class="auth_mail" title="E-mail the corresponding author} ; Xiaosheng Zhuang^d ; ^{xzhuang7@cityu.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：42C40 ; 41A15 ; 94A12 ; 93C55 ; 93C95 ; 93C30
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：41
• 期：1
• 页码：266-296
• 全文大小：589 K

文摘

Motivated by the need of short FIR filters for perfect-reconstruction multirate systems, the main objective of this paper is to derive the shortest filters for such filter banks with M$\mathsf{M}$ channels, for any integer M⩾2$\mathsf{M}⩾2$, based on the M$\mathsf{M}$-dilated refinement sequence p_m${\mathsf{p}}_m$ of the mth order cardinal B-spline. By imposing the additional constraint of ℓ  th order sum rule on the M$\mathsf{M}$-dual low-pass sequence a_m${\mathsf{a}}_m$, the smoothness property of the M$\mathsf{M}$-dual scaling function, along with its corresponding analysis wavelets, is studied, and consequently yielding the ℓ  th order vanishing moment for each of the M−1$\mathsf{M}-1$ synthesis (spline) wavelets. Several illustrative examples and tables of the filter systems are also included in this paper.