S-transform based on optimally concentrated time-limited and band-limited Windows

S-transform (ST) is a tool for time-frequency analysis. Improving the energy concentration in time-frequency domain remains a major challenge in ST. Choosing a time-limited narrow window is beneficial for precisely resolving spectral components in time, and similarly a band-limited window can provide improved resolvability in frequency domain. However, limiting an arbitrary window in one domain results in unwanted spreading in other domain. To this extent, two discrete optimal windows, time-limited and band-limited with minimum spread in other respective domain are designed in this paper. By extending the windows, two variants of ST, namely time-limited ST (TST) and band-limited ST (BST) are proposed. The proposed variants of ST are particularly beneficial for the applications where a very precise resolution is desired in either time or frequency domain. The efficacy of proposed approaches is evaluated on a set of test as well as practical signals. The simulation results indicate that the proposed TST and BST can provide higher energy concentration in time and frequency domains, respectively as compared to conventional ST and its variants. In addition to that, the proposed variants of ST provides more flexibility in choosing window width in time and frequency domain.