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中文摘要：
基于两通道滤波器组构建的子带信号处理方法已在图像、语音信号处理中得到广泛的应用．本文从分数阶傅里叶域多抽样率信号处理基本理论和分数阶卷积定理出发，推导了分数阶傅里叶域两通道滤波器组准确重建的基本条件，并基于传统傅里叶域有限长标准正交镜像滤波器组和共轭正交镜像滤波器组的原型滤波器设计了分数阶傅里叶域标准正交镜像滤波器组和共轭正交镜像滤波器组．本文所提出的结论为分数阶傅里叶域滤波器组理论的建立提供了基本依据，同时也为分数阶傅里叶变换在图像、语音信号处理等工程实践中的应用奠定了理论基础．最后，仿真实验验证了所提分数阶傅里叶域滤波器设计方法的有效性．
英文摘要：
Sub-band coders have been applied widely in the image processing and speech signal processing. Two-channel multirate digital filter banks are the basic components of the tree-structured sub-band coders. This paper proposes the perfect recon-struction condition of two channel multirate filter banks in the fractional Fourier domain（FRFD）,based on the theorem for FRFD analysis of signal sampling rote conversion and fractional convolution theory. Then, this paper illustrates that it is possible to design two-channel FIR Quadrature Mirror Filter Banks（QMFB） and Conjugate Quadrature Mirror Filter Banks（CQMFB）through the prototype filters of FIR QMFB and CQMFB in Fourier domain. The proposed theorems in this study advance the generalization of filter banks in FRFD, which are the bases of the applications of FRFY in the practices, such as image processing, speech signal processing, etc. Finally, the effectiveness of the proposed methods is verified by the simulations.
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