Frame Operator Approach for Designing Discrete-Time Multiple Short-Time Fourier Transform and Its Time-Frequency Distribution

摘要

This paper presents a discrete-time multiple short-time Fourier transform (MSTFT) suitable for a time-frequency analysis and synthesis of discrete-time nonstationary signals. An overcomplete set of multiple windows is used for a frame constitution in l~2(Z) so that higher quality signal analysis and perfect reconstruction of the signal are achieved. A design method for a prototype window is given where the window can satisfy regularity condition and have a flexible, good time and frequency characteristic under constraint of the uncertainty principle. A dual frame is constructed using the prototype windows in the framework of a frame operator method. Efficient implementation structures for the MSTFT and its inverse transform appropriate for real time numerical processing is presented. Simulation results are given to illustrate the effectiveness for design of the MSTFT. The performance advantages as a new signal analysis tool are demonstrated with an experimental signal.