| Abstract: | Detecting the number of signals and estimating the parameters of the signals is an important problem in signal processing. Quite a number of papers appeared in the last twenty years regarding the estimation of the parameters of the sinusoidal components but not that much of attention has been given in estimating the number of terms present in a sinusoidal signal. Fuchs developed a criterion based on the perturbation analysis of the data auto correlation matrix to estimate the number of sinusoids, which is in some sense a subjective-based method. Recently Reddy and Biradar proposed two criteria based on AIC and MDL and developed an analytical framework for analyzing the performance of these criteria. In this paper we develop a method using the extended order modelling and singular value decomposition technique similar to that of Reddy and Biradar. We use penalty function technique but instead of using any fixed penalty function like AIC or MDL, a class of penalty functions satisfying some special properties has been used. We prove that any penalty function from that special class will give consistent estimate under the assumptions that the error random variables are independent and identically distributed with mean zero and finite variance. We also obtain the probabilities of wrong detection for any particular penalty function under somewhat weaker assumptions than that of Reddy and Biradar of Kaveh et al. It gives some idea to choose the proper penalty function for any particular model. Simulations are performed to verify the usefulness of the analysis and to compare our methods with the existing ones. |
