Estimating the number of sinusoids in additive white-noise

For a random process that can be modeled as a sum of real sinusoids in white noise, we address the problem of the estimation of the number of sinusoids. The test we propose uses the eigen-decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis. The estimator is shown to resolve closely spaced sinusoids at quite low signal -to- noise ratios.