A windowing condition for characterization of finite signals from spectral phase or magnitude

Reconstruction of a signal from its spectral phase or magnitude is in general an ill-posed problem. Various conditions restricting the class of signals under consideration have been shown to be su cient to regularize the problem so that a unique (or essentially unique) signal corresponds to any given spectral magnitude or spectral phase function. This paper shows that a nite discretetime signal is characterized by its spectral magnitude (or phase) and the spectral magnitude (or phase) of an ancillary signal obtained by windowing the original signal.