Fast calculation of the Choi-Williams time-frequency distribution

Abstract

The method presented allows faster calculation of any time-frequency distribution with a kernel that can be formulated in the time-lag plane. Specific examples are the Wigner and Choi-Williams distributions. The Choi-Williams distribution (CWD) uses an exponential kernel in the generalized class of bilinear time-frequency distributions to achieve a reduction in the cross-term components of the distribution. Matrix manipulations provide an intuitive approach and, when combined with parallel processing, improve the processing speed to allow real-time calculations of the CWD. The use of an outer product matrix with a weighting matrix is particularly useful when evaluating different weighting parameters. For any given signal, the outer product matrix needs to be calculated just once. The various weighting matrices can be stored and used with any signal when needed. Parallel processing architectures allow implementation of the algorithm with speeds that are appropriate for real-time, running window calculations. >