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-Raphsonʹs method. A simulation example is given showing the synthesized signal over the first few iterations.