The exact estimation error analysis in the instantaneous frequency estimation by using quadratic time-frequency distributions

Abstract

General performance analysis of the instantaneous frequency (IF) estimators, for an arbitrary frequency modulated (FM) signal, is presented. Shift covariant class of quadratic time-frequency distributions as IF estimators are considered. The expressions for the IF estimator variance in the cases of white stationary and white nonstationary additive noises are derived. As special cases of this analisis, the well known results for the Wigner distribution and linear FM signal, and for the spectrogram of signals whose IF may be considered as a constant within the lag window, are presented. In addition, analysis of the linear FM signal is performed in the cases of commonly used distributions, such as spectrogram, Choi-Williams, BornJordan. The quite simple expression for variance of spectrogram of this signal (that is highly signal dependent) is derived. The presented expressions are checked statistically. It has been shown that the reduced interference distributions outperform the Wigner distribution, but only in the case when the IF is constant or its variations are small.