Estimation of close sinusoids in colored noise and model discrimination
Abstract
This paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown. Earlier attempts have assumed the additive noise to be independent. Next, decision rules were developed for checking whether the observed signal has only one sinusoid or two close sinusoids. All of the earlier studies assumed that there are two close sinusoids in the signal. Another model discrimination problem considered is the determination of the causal structure of the observed periodicity. A rule is given to test whether the observation comes from a sinusoid plus additive noise, possibly colored, or from a stationary autoregressive model. In addition, a numerical study showing the efficacy of the robust estimation procedure for estimating the two fequencies and the decision rules for checking the number of dominant frequencies and the casual mechanism is presented. Finally, the proposed method is compared to wellknown methods used for two close sinusoids in white noise.
 Publication:

IEEE Transactions on Acoustics Speech and Signal Processing
 Pub Date:
 March 1987
 Bibcode:
 1987ITASS..35..328C
 Keywords:

 Autoregressive Processes;
 Maximum Likelihood Estimates;
 Noise Spectra;
 Signal Processing;
 Sine Waves;
 Stochastic Processes;
 Bayes Theorem;
 Least Squares Method;
 Probability Density Functions;
 Robustness (Mathematics);
 Signal To Noise Ratios;
 Communications and Radar