Instantaneous Frequency Estimation Using Higher Order-Wigner Distributions with Data-Driven Order and Window Length

Abstract—The-Wigner distributions are defined in order to improve the concentration of signal’s time–frequency representation. For a finite distribution order and nonlinear instantaneous frequency (IF) it gives bi-ased IF estimates. In the case of noisy signals the optimal window length and distribution order depend on the noise variance and unknown IF. In this correspondence an adaptive IF estimator with the time-varying and data-driven window length and distribution order is developed. Based on the analysis that has been done here, lower order time–frequency distribu-tions are introduced. Index Terms—Estimation, instantaneous frequency, time–frequency analysis, Wigner distribution, window optimization. I