Simulation results are presented to compare the effectiveness of various windowing functions for the generalized correlator when a strong spectral peak or sinusoid is present. In this case, the time delay of the desired source and of the interfering sinusoid are allowed to be different. The results show that all windows except HBII and SCOT deteriorate markedly. These two windows remain robust to the ambiguity problems presented by the sinusoid, independent of whether the spectral peak is included in the signal spectrum or in the noise spectrum. Also, window HBII performs better than SCOT in terms of probability of correct detection, variance of time delay, and SNR threshold.

A nonlinear adaptive method is presented for filtering a signal which is corrupted by spikes which take discrete values Mi with probability Pi at random points in time. An unsupervised learning technique is used to estimate the unknown parameters Mi, Pi, and oi. The spikes are then removed using a Bayes classifier. A theoretical and experimental comparison with the MMSE linear filter is presented.

Various optimum and sub-optimum filters have been added to the basic cross-correlator in order to enhance its time delay estimation capability in the presence of noise. These pre-detection filters include the Hannan-Thomson, the Eckart, the Smoothed Coherence Transform, some least-squares, and two optimum filters recently derived by the authors. Here, a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal and noise ratio and signal and noise bandwidths. The results define the actual enhancement in time delay detection when using the optimum filters and the amount of performance degradation from the optimum for the other filters. The rank ordering of the filters is carried out. Histograms of the time delay estimates, their mean and variance are presented. Confirmation of analytical predictions is noted.

Often, the cepstrum has been used when estimating the time delay r between elements of a composite signal embedded in noise,n(t). Here a probabilistic analysis is conducted dealing with the effect of stationary Gaussian noise on the characteristics of such a nonlinear processor. The input noise,n(t)is reflected at the cepstrum's output as: 1) modulationM_{1}(\omega)of sinusoidal information carrier with subsequent reduction in the height of echo peak at\tau; and 2) generation of background noises\hat{phi}(\omega)and\hat{psi}(\omega)with tendency to obscure that echo peak. The resulting probabilities of these terms are derived. The expected mean and standard deviation of reduction in the peak level at\taudue to noise are analytically described. Similar statistical measures on the background noise are also obtained. The results point out the dependence of the-statistical measures upon the pointwise variation of input signal to noise spectra. Thus the total signal power to total noise power(S/N)alone is an insufficient measure for setting the cepstrum performance, and relative bandwidths of signal and noise are also needed. The detection probabilityP_{D}of a peak corresponding to\tauis calculated for exponential spectra with equal bandwidths in signal and noise and with echo strengtha = 0.4; P_{D}is found to be close to one for anSINgreater than -4 dB; deterioration in detection is found to be rapid with thresholding near anS/N \sim -6db whereP_{D}falls to 0.3.