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

Shigeo WADA  Hideki YAGI  Hiroshi INABA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.6   pp.977-986
Publication Date: 1997/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing Theories and Applications Based on Modelling of Nonstationary Processes)
short-time Fourier transform,  frame operator,  multirate system,  spectrogram,  

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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 in used for a frame constitution in l2 (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.