Signal synthesis from Wigner distribution

The problem of synthesizing a signal from a modified or specified Wigner distribution function is considered. This problem arises in signal separation, time frequency filtering, window and filter designs. The modified or specified time frequency function may not correspond to a valid Wigner function, thus our synthesis problem is formulated as approximately a two-dimensional function as a product of two one-dimensional function by using least squares procedure. The first procedure involves expressing a time-frequency function as a bilinear combination of basis auto and cross Wigner functions. The least squares approximation leads to an eigenvalue-eigenvector decomposition of a symmetric matrix. The second procedure involves the approximation of a pre-computed matrix as an outer product of two vectors.