从多相滤波视角阐释滑窗DFT多路输出的特性

Explanation on the Characteristics of Multiplex Output Based on Sliding Window DFT from the Perspective of Multiphase Filtering

滑窗离散傅里叶变换(Discrete Fourier Transform, DFT)是目前工程上最常用的信号时频分析工具,但目前对滑窗重叠度以及滑窗DFT的物理意义的阐释并不透彻。针对这一问题,在简要回顾了两种形式的滑窗DFT和两种形式的多相滤波实现流程的基础上,从多相滤波视角对滑窗DFT多路输出的特性进行了全新的阐释,指出了窗口不交叠的滑窗DFT与简化形式的多相滤波之间的等价关系,以及窗口部分重叠的滑窗DFT与常规形式的多相滤波之间的关联关系,并通过仿真验证了上述分析的正确性与有效性。从而为基于滑窗DFT的多信道并行滤波处理、信号时频分析、子信道信号提取与分离等工程应用提供了理论指导与应用参考。

Sliding window Discrete Fourier Transform(DFT)is the most commonly used signal timefrequency analysis tool in engineering,but the explanation in existing literatures on its sliding window overlap and the physical meaning is not thorough enough.In response to this issue,after a brief review of two forms of sliding window DFT and two forms of multiphase filtering implementation processes,the characteristics of the multiplex output based on sliding window DFT are newly explained from the perspective of multiphase filtering.The equivalence relationship between sliding window DFT with nonoverlapping windows and simplified multiphase filtering is pointed out,as well as the correlation between sliding window DFT with partly overlapping windows and conventional multiphase filtering.The correctness and effectiveness of above analysis are verified through simulations,which provides theoretical guidance and application reference for engineering applications such as multi-channel parallel filtering processing,signal time-frequency analysis,sub-channel signal extraction and separation based on sliding window DFT.