Effective calculation of finite frame operator for the multiple short-time Fourier transform

In this paper, effective methods to calculate finite dual frame for the short-time Fourier expansion (STFE) in l(2)(Z) are proposed when arbitrary finite frame is given. Based on a relationship between the prototype window used for generating frame window and the dual prototype window used for generating dual frame window, two effective numerical methods with a finite frame operator are shown to obtain finite support dual frame windows in discrete-time domain formulation. The methods can be applied to construct the multiple STFE (MSTFE) suitable for a time-frequency analysis and synthesis of nonstationary signals. Simulation results are given to verify the effectiveness of the design of dual frame windows for composing the MSTFE.