XWD-algorithm for the instantaneous frequency estimation revisited: Statistical analysis

• Statistical analysis of the XWD-based IF estimator.
• Expressions for bias and variance introduced.
• The adaptive algorithm for the IF estimation proposed.
• Numerical analysis confirms findings.

In this paper we reconsider the cross-Wigner distribution (XWD), one of the first techniques proposed in time-frequency (TF) analysis for the instantaneous frequency (IF) estimation under low signal-to-noise ratio (SNR). Its realization was based on an iterative procedure, while its performance had been assessed through the simulations only. In this paper, we derive asymptotic performance of the XWD-based IF estimator. The obtained results are used to develop an algorithm for the selection of an adaptive window width in the XWD estimator, producing a trade-off between the bias and variance. The results obtained using this algorithm are compared with the state-of-the-art in the field.