基于谱分解技术的两通道因果稳定IIR滤波器组的设计

doi:10.3969/j.issn.0253-2778.2015.01.005

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (1): 27-33.DOI: 10.3969/j.issn.0253-2778.2015.01.005

• 论著 • 上一篇

基于谱分解技术的两通道因果稳定IIR滤波器组的设计

殷仕淑，高玲，于帅珍

安徽财经大学电子信息工程系，安徽蚌埠 233041

收稿日期:2013-12-17 修回日期:2014-10-09 接受日期:2014-10-09 出版日期:2014-10-09 发布日期:2014-10-09

Design of two-channel causal-stable IIR filter banks by spectral factorization

YIN Shishu, GAO ling, YU Shuaizhen

Dept. of Electronic and Information Engineering, Anhui university of Finance & Economic, Bengbu, 233041, China

Received:2013-12-17 Revised:2014-10-09 Accepted:2014-10-09 Online:2014-10-09 Published:2014-10-09
Contact: YIN Shishu
About author:YIN Shishu (corresponding author), female, born in 1973, PhD. Research field: multirate signal processing, filter banks, wavelets, image signal processing. E-mail: ssyin@eee.hku.hk
Supported by:
Supported by the National Natural Science Foundation of China (61102118).

摘要/Abstract

摘要： 提出一种新的两通道因果稳定IIR滤波器组的设计方法.首先基于所定义的一种余弦滚降IIR滤波器，两通道滤波器组所要求的平坦条件完全被满足；其次该方法是依赖于分析滤波器的功率谱特性，而不是该滤波器的幅度频率特性来设计滤波器组.IIR滤波器的设计问题可转化成一个准凸问题，采用凸优化算法来求解；然后对所得优化解进行谱分解，得到目标滤波器组.该滤波器组具有合理的完全重构误差，并且其多相因子的分母相同，简化了完全重构条件.采用该滤波器组作为约束非线性优化法的有效初值，进一步优化得到完全重构2通道IIR滤波器组.

关键词: 因果稳定的IIR滤波器, 余弦滚降, 滤波器组, 近似完全重构和完全重构, 谱分解

Abstract: A new method was proposed for designing two-channel filter banks (FBs) with causal-stable IIR filters. By using IIR filters with a cosine-rolloff transition band, the flatness condition required for two-channel NPR FB was automatically satisfied. Instead of designing the frequency magnitude responses of the analysis filters, the power spectra of the desired filters were designed by solving a quasi-convex problem. When the solution was found, the analysis filters desired can be obtained by spectral factorization. The polyphase components of the analysis filters were assumed to have an identical denominator to simplify the PR condition. Two-channel NPR IIR FB so obtained has a reasonably low reconstruction error and can be employed as the initial guess to constrained nonlinear optimization software for designing the PR IIR FB.

Key words: causal stable IIR filters, cosine-rolloff transition band, filter banks, perfect and nearly perfect reconstruction, spectral factorization

中图分类号:

TN713

殷仕淑，高玲，于帅珍. 基于谱分解技术的两通道因果稳定IIR滤波器组的设计[J]. 中国科学技术大学学报, 2015, 45(1): 27-33.

YIN Shishu, GAO ling, YU Shuaizhen. Design of two-channel causal-stable IIR filter banks by spectral factorization[J]. Journal of University of Science and Technology of China, 2015, 45(1): 27-33.

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基于谱分解技术的两通道因果稳定IIR滤波器组的设计

Design of two-channel causal-stable IIR filter banks by spectral factorization

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