短时分数阶傅里叶变换的基本性质

作为一种不会对信号时频结构在解线调时产生压缩扭曲的线性时频分析工具,短时分数阶傅里叶变换(STFrFT)相比于分数阶傅里叶变换更适于处理多项式相位信号.证明了短时分数阶傅里叶变换的一些基本性质,例如:重构条件和帕塞瓦尔定理等.以chirp信号为例给出了STFrFT的窗函数和窗口参数的选择依据.本文结论为短时分数阶傅里叶变换的应用提供参考.

Basic Properties of Short-Time Fractional Fourier Transform

As a novel tool for time-frequency analysis,the short-time fractional Fourier transform(STFrFT)does not lead to the distortion while achieving dechirping.Thus,STFrFT is more appropriate to process polynomial phase signals than the fractional Fourier transform (FrFT).Some basic properties of STFrFT,such as reconstruction condition,Parseval principle and so on are proved.The selection principles of the window function and its parameters are given by a chirp signal.The obtained conclusion provides a reference for STFTFT application.