ALIAS-FREE GENERALIZED DISCRETE-TIME TIME-FREQUENCY DISTRIBUTIONS

Many of the bilinear time-frequency representations suggested so far are members of Cohen's class of generalized time-frequency distributions. For practical implementation of members of Cohen's class, a generalized discrete-time time-frequency distribution has been defined and used. In this paper, we introduce a new definition of generalized discrete-time time-frequency distribution. Unlike the existing one, the new definition utilizes all of the outer product terms from a data sequence, so that one can avoid aliasing. Furthermore, 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 new formulation provides a unified framework for implementing members of Cohen's class, which was formulated in the continuous-time domain. We discuss some requirements for the discrete-time kernel in the new approach in association with desirable distribution properties. Some experimental results are provided to illustrate the features of the proposed method.