This paper presents effective methods to calculate dual frame of the short-time Fourier expansion (STFE) in l2(Z). Based on a relationship between the prototype window used for generating a frame and the dual prototype window used for generating a dual frame in the STFE, two useful numerical methods with a finite frame operator are proposed to obtain finite support dual frames in time domain formulation. The methods can be used to construct the multiple STFE (MSTFE) suitable for a time-frequency analysis, synthesis and coding of discrete-time nonstationary signals. Numerical simulation results are given to verify the effectiveness of the calculation of dual frame.

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.