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从分数阶圆周卷积定理和离散信号在分数阶傅里叶域的chirp周期性出发,研究了分数阶傅里叶域循环多抽样率信号处理理论,包括有限长非平稳信号循环内插和循环抽取的分数阶傅里叶域分析,分数阶傅里叶域循环抽取和循环内插的恒等关系、分数阶傅里叶域循环滤波器组的多相结构和准确重建条件,并在此基础上提出了分数阶傅里叶域M通道准确重建循环滤波器组和分数阶傅里叶域chirp调制循环滤波器组的设计方法.所提理论丰富了分数阶傅里叶域多抽样率信号处理理论体系,也为分数阶傅里叶域滤波器组理论在数字图像处理等有限长离散信号处理领域中的应用奠定了基础.最后,通过仿真实验验证了所提分数阶傅里叶域循环滤波器组设计方法的有效性.
Based on the fractional order circular convolution theorem and the chirp periodicity of discrete signals in fractional Fourier domain, the theory of fractional Fourier domain cyclic multisample rate signal processing is studied, including finite length non-stationary signal cycle interpolation and cycle The extracted fractional Fourier domain analysis, the fractional Fourier domain circular extraction and the relationship between the cyclic interpolation, the fractional Fourier domain of the filter bank of multi-phase structure and accurate reconstruction conditions, and based on this The design method of fractional order Fourier domain M-channel accurate reconstruction cyclic filter bank and fractional Fourier domain chirp modulation cyclic filter bank is proposed. The proposed theory enriches the performance of fractional Fourier domain multi-sample rate signal processing Theoretical system, but also for fractional Fourier domain filter group theory in digital image processing and other finite signal processing applications in the field of finite length.Finally, the simulation results show that the proposed fractional Fourier domain loop filter The effectiveness of the design method of the group.