Time-frequency readability enhancement of compact support kernel-based distributions using image post-processing: Application to instantaneous frequency estimation of M-ary frequency shift keying signals

Time-frequency distributions (TFDs) based on time-lag kernels with compact support (KCS) have proved their high performance in terms of resolution and crossterms suppression. However, as for all kernel-based quadratic TFDs, these distributions suffer from spreading out signal terms. This is due to the unavoidable smoothing effects of the kernel in the ambiguity domain. The main objective of this paper is to improve concentration, interference rejection and so time-frequency localization of this representation class. The latter has the advantage of being tuned using a single parameter while external windows are no longer needed. The KCS-TFDs, referred to as KCSDs, are first optimized using a selection of the most used objective performance measures in the literature. Important signal features are extracted as well through analysis of time slice plots. The obtained TF diagrams are then enhanced using a specific method that includes two-dimensional Wiener filter, automatic binarization and morphological image processing techniques. The enhanced plots are compared to those obtained from the original TFDs using several tests on real-life and multicomponent frequency modulated (FM) signals including the noise effects. Moreover, a comparative study involving a selection of the best-performing reassignment time-frequency distributions is provided. The obtained results show a significant improvement of concentration, time-frequency localization of the autoterms as well as interference and noise suppression. As viable applications, the proposed approach is used first to instantaneous frequency (IF) estimation of several synthetic and real-life M-ary frequency shift keying (MFSK) signals. It is shown that the IF estimator from the enhanced plots performs better than smoothed pseudo Wigner-Ville distribution (SPWVD) and reassignment post-processing-based TFDs in terms of mainlobe width (MLW) and variance, respectively, even at low signal-to-noise ratio (SNR). On the other hand, time-frequency characterization of continuous wave linear frequency modulation (CW-LFM) and pulse linear FM (PLFM) radar signals is also investigated.