Performance analysis and computational cost evaluation of high-resolution time-frequency distributions derived from compact support time-lag kernels

This paper considers the objective performance evaluation of kernel-based time-frequency distributions (TFDs) using several concentration performance measures and resolution examination through a deep analysis of time slice plots. On the other hand, the numerical complexity of each TFD is evaluated; a parameter that is particularly critical when real-time implementation is intended. The performance of TFDs based on time-lag kernels with compact support (KCS) namely the Cheriet-Belouchrani (CB), the separable (CB) (SCB) and the polynomial CB (PCB) TFDs is compared to the well-known kernel-based TFDs using several tests on real-life and multicomponent signals with linear and nonlinear frequency modulation (FM) components including the noise effects and the influence of the kernel length. In all presented examples, the time-lag KCS TFDs, and particularly the PCB TFD, provide the best compromise between highest autoterm resolution and interference rejection while still requiring moderate computational costs thanks to the compact support nature of their kernels that reduces the number of points needing computation. On the other hand, the derived distributions do not require any smoothing window neither in time nor frequency in order to achieve the best time-frequency resolution. Furthermore, they have an extremely interesting practical advantage since their adjustment is performed by simply changing a single parameter which is integer for the PCB TFD.