Optimisation of the Realisation of Quadratic Discrete Time-Frequency Distributions as a MATLAB Toolbox

Abstract

An optimised time-frequency signal analysis software tool is presented here as a MATLAB toolbox. This toolbox is implemented using existing and novel methods for a specific class of Time-Frequency Distributions (TFDs) called quadratic TFDs. This is first applied to a TFD called the Wigner-Ville Distribution (WVD), as all other quadratic TFDs can be represented as a smoothed (in both time and frequency) version of the WVD. This method is then extended to the general quadratic TFD case, where the complete implementation optimises both simulation speed and memory usage. Also some quadratic TFDs can be represented in their direct form, such as the Spectrogram and Rihaczek distribution. The optimization of the implementation of these distributions is also examined.