SVD-BASED INFORMATION-THEORETIC CRITERIA FOR DETECTION OF THE NUMBER OF DAMPED UNDAMPED SINUSOIDS AND THEIR PERFORMANCE ANALYSIS

Recently, Wax and Kailath developed information theoretic criteria for detection of the number of signals received by a sensor array. More r ecently, Fuchs developed a criterion, based on the perturbation analys is of the data autocorrelation matrix, for detecting the number of sin usoids. In this paper, following the information theoretic approach to model selection, we first develop criteria for detection of the numbe r of damped/undamped sinusoids. These criteria are matched to the sing ular value decomposition (SVD) based methods, such as modified forward /backward and forward-backward linear prediction, so well that the ext ra computations needed over and above those required for computing the SVD are marginal. Next, we develop an analytical framework for analyz ing the performance of these criteria, following the assumptions made by Wang and Kaveh and the corrections given by Zhang et al. In the dev elopment of the analysis, we make some approximations which become bet ter for large signal-to-noise ratio. Simulations are used to verify th e usefulness of the analysis, and to compare the performance of our me thod with that of Fuchs.