Separable kernel design for bilinear time- frequency analysis of digital modulation signals

Time-frequency distributions (TFD's) are powerful tools to re present the energy content of time-varying signal in both time and frequency domain simultaneously. One of the limitations in this method is the presence of interference in the time-frequency representations (TFR's) caused by the cross terms. Various methods have been researched to remove these cross-terms. However, there is no single TFD with a fixed window or kernel that could perform well for all type of signals. In this paper, separable kernel with its parameters determined mathematically from the digital modulated signal is designed. This optimum kernel is capable of removing the cross-terms and maintaining accurate time-frequency representation for ASK, FSK and M-ary FSK signals. It is shown that signals with different parameters, such as frequencies and bit-duration, require different setting in order to get the optimum time-frequency representation. A simple guideline to determine the separable kernel parameters are presented.