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中文摘要：
分数阶傅里叶变换相对于传统的傅里叶变换具有灵活的时频分析特性,在最优分数阶傅里叶域进行滤波可以实现对某些非平稳信号的最优检测和参数估计以及对某些干扰和噪声的滤除.分数阶傅里叶域滤波器组理论的提出弥补了分数阶傅里叶域滤波不具备多尺度分析以及运算量过大的缺点,但现有的分数阶傅里叶域准确重建滤波器组设计方法不具备形式一般化的特点,很难满足很多实际工程的需要.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,推导出了分数阶傅里叶域准确重建滤波器组的一般化设计方法,为分数阶傅里叶域滤波器组理论在实际工程中的推广应用奠定了理论基础.最后,仿真实验验证了本文所提分数阶傅里叶域滤波器组一般化设计方法的有效性.
英文摘要：
The fractional Fourier transform（FRFT）is of better time frequency analysis character than the traditional Fourier transform.The filtering in the optimal fractional Fourier domain（FRFD）can estimate some special cases of non-stationary signals and systems with minimum mean square error.The theorem for the multirate filter bank in the FRFD leads to the efficient structure of filtering in the FRFD and the multi-resolution analysis of signal in the FRFD.But the existing perfect reconstruction filter banks in the FRFD are of special form, which cannot satisfy some practices. This paper proposes the generalized design method for the perfect reconstruction filter banks in the FRFD based on the FRFD analysis of sampling rate conversion and the fractional convolution theo- rem, which are the basis of the applications of filter bank theory in the FRFD. At last, the simulations verify the generalized design method.
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