Alias-free generalized discrete-time time-frequency distributions

A definition of generalized discrete-time time-frequency distribution that utilizes all of the outer product terms from a data sequence, so that one can avoid aliasing, is introduced. The new approach provides (1) proper implementation of the discrete-time spectrogram, (2) correct evaluation of the instantaneous frequency of the underlying continuous-time signal, and (3) correct frequency marginal. The formulation provides a unified framework for implementing members of Cohen´s class, which was formulated in the continuous-time domain. Some requirements for the discrete-time kernel in the new approach are discussed in association with desirable distribution properties. Some experimental results are provided to illustrate the features of the proposed method