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.

We propose concepts of Paley-Wiener multiresolution analysis and Paley-Wiener wavelet frame based on general, not limited to dyadic, dilations of functions. Such a wavelet frame is an extension both of the Shannon wavelet basis and the Journe-Meyer wavelet basis. A concept of "natural" Paley-Wiener wavelet frame is also proposed to clarify whether a Paley-Wiener wavelet frame can naturally express functions from the point of view of the multiresolution analysis. A method of constructing a natural Paley-Wiener wavelet frame is given. By using this method, illustrative examples of Paley-Wiener wavelet frames with general scales are provided. Finally, we show that functions can be more efficiently expressed by using a Paley-Wiener wavelet frame with general scales.