【作者】 杨晓慧；

【导师】 李登峰；

【作者基本信息】 河南大学 ， 基础数学， 2004， 硕士

【摘要】 由于多速率数字滤波技术可有效地降低信号的处理复杂度、加快数据的传输率和提高存储量等，所以它在图像编码、语音编码及通信等众多领域具有广泛的应用。本论文主要探索了多速率滤波器组的设计方法。它由五章组成。 第一章简述了多速率滤波器组的基本问题、发展历史和研究现状。 第二章总结说明了小波、多尺度分析与滤波器组之间的内在联系。 第三章是本文的主要内容之一。由于M带小波比2带小波分析信号更细致、更紧凑，而M带小波可由迭代的M通道滤波器组获得，所以本章分析了一种两通道线性相位完全重构无限脉冲响应滤波器组的有效设计方法，希望可推广用于M(M＞2)通道。论证说明这种方法不能直接推广用于M(M＞2)通道，其局限性在于只对两通道有效；最后给出了用此方法设计两通道线性相位完全重构有限脉冲响应滤波器组的详细过程。 第四章是论文的另一重要内容。讨论了一种时域设计偶数通道双正交线性相位完全重构有限脉冲响应滤波器组的方法同样适用于奇数通道；并把此算法应用于设计长度不相等的两通道双正交线性相位完全重构有限脉冲响应滤波器组。 第五章是本文的结束语，对文章给出总结，并对以后的研究方向做了展望。更多还原

【Abstract】 The use of multiple sampling rates offers many advantages, such as reducing computational complexity for a given task, speeding up transmission rate, and/or raising storage capacity. So the applications of multirate digital filter technology have been found in subband coding of images and speeches, communications, and in many other fields. The thesis is mainly about the design methods for multirate filter banks.Chapter 1 summarizes the basic question, developing history and present research situation of the multirate filter banks.In chapter 2, the author gives the inner connection of wavelets, MRA and filter banks.Chapter 3 is one of the important contents of the thesis. Because multi-band wavelet can describe signal more delicately and more compactly than two-band wavelet, and multi-band wavelet can be derived from the infinite iteration of multi-channel filter banks. By means of a detailed discussion for a effective design method of linear phase PR IIR filter banks, the author obtain that the method is only fit for two-channel filter banks, but can’t be extended to arbitrary M-channel(M > 2) filter banks. Moreover, the detailed design process of two-channel FIR filter banks is presented by using the modulated method.Chapter 4 is the other important contents of the thesis. By analyzing an effective time-domain design method of even-channel biorthogonal linear-phase PR FIR filter banks, the chapter discusses the case of odd-channel, and modulated the design method to two-channel unequal-length biorthogonal linear-phase PR FIR filter banks.In chapter 5, the conclusion and the expectation of the article are given.更多还原