Improvement of Energy Concentration in S-transform using Maximally Concentrated Window

Time-frequency representation (TFR) of a signal using S-transform (ST) provides detailed information about the local spectrum at any instant of time. One of the major limitations with conventional ST is poor time resolution at low frequencies due to very long taper of Gaussian window. It restricts the application of ST in precisely resolving the signal components in time and finite event detection. To counter this problem, we propose a variant of ST namely time-limited ST (TST) based on zero order prolate spheroidal wave function. For practical implementation, discrete counterparts of the TST is proposed based on zero order discrete prolate spheroidal sequence. This technique is particularly beneficial for effectively detecting certain finite duration event and precisely localizing the initiation and termination of an event. The simulation results indicate that the proposed TST can precisely resolve signal components in time, and simultaneously provide maximum concentration in freuuency.