Instantaneous frequency estimation based on directionally smoothed pseudo-Wigner-Ville distribution bank

In the cases of low signal-to-noise ratios (SNRs), estimating the instantaneous frequency (IF) curves of signals of interest is an interesting topic with many practical applications. Most of the existing methods are based on quadratic time-frequency (TF) distributions, which, however, yield a number of outliers in the cases of low SNRs. In this paper, we construct a new family of TF distributions, namely, the joint distributions, to estimate the IF curves in order to reduce outliers in the cases of low SNRs. The construction of the joint distributions is based on the definition of the directionally smoothed pseudo-Wigner-Ville distributions (DSPWVD) and pointwise adaptive weight averaging of a bank of DSPWVDs with different directions. The segments of the IF curve whose directions are close to that of the DSPWVD can be highlighted by each DSPWVD and the entire IF curve will be enhanced by the joint TF distribution. Simulation results show that the IF estimator based on the joint distributions outperforms that using quadratic TF distributions and the adaptive optimal adaptive kernel distribution in the cases of low SNRs.