Synthesis of discrete-time discrete-frequency Wigner distribution

A recursive algorithm is proposed for synthesizing a discrete-time periodic signal from a specified discrete-time discrete-frequency Wigner distribution by minimizing the error in the cyclic outer product. Equating the gradient of the error with respect to signal samples to zero results in a set of nonlinear simultaneous equations, which are solved using Newton-Raphson's method. A simulation example is given showing the synthesized signal over the first few iterations.

[1]  Bijan G. Mobasseri,et al.  Digital watermarking in joint time-frequency domain , 2002, Proceedings. International Conference on Image Processing.

[2]  H. T. Morsche,et al.  Integral representations of affine transformations in phase space with an application to energy localization problems , 1999 .

[3]  Thomas W. Parks,et al.  Discrete-time, discrete-frequency, time-frequency analysis , 1998, IEEE Trans. Signal Process..

[4]  Thomas W. Parks,et al.  The Weyl correspondence and time-frequency analysis , 1994, IEEE Trans. Signal Process..

[5]  Gloria Faye Boudreaux-Bartels,et al.  An algorithm for synthesizing signals from partial time-frequency models using the cross Wigner distribution , 1993, IEEE Trans. Signal Process..

[6]  Werner Krattenthaler,et al.  Bilinear signal synthesis , 1992, IEEE Trans. Signal Process..

[7]  B. V. K. Vijaya Kumar,et al.  Discrete Wigner synthesis , 1986 .

[8]  Thomas W. Parks,et al.  Time-varying filtering and signal estimation using Wigner distribution synthesis techniques , 1986, IEEE Trans. Acoust. Speech Signal Process..

[9]  Kai-Bor Yu,et al.  Signal synthesis from Wigner distribution , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Thomas W. Parks,et al.  Signal estimation using modified Wigner distributions , 1984, ICASSP.

[11]  D. Slepian.  Some comments on Fourier analysis, uncertainty and modeling , 1983 .

[12]  D. Slepian.  Some Asymptotic Expansions for Prolate Spheroidal Wave Functions , 1965 .