Noise analysis in Toeplitz and Hankel kernels for estimating time-varying spectra

An analysis of noise influence to time-varying spectra estimators is presented. Hankel and Toeplitz kernel forms of distributions are considered. It is shown that these two forms of kernels have the same variance, if the windows have the same form. Since the Hankel kernel results in a highly concentrated distribution for a noisy, frequency-modulated signal, this form can be more reliable for the estimation of signal parameters in noise. The results are generalized to multiplicative noise; in this case, the same conclusions hold for frequency-modulated signals.