Simultaneous detection and frequency estimation of sinusoidal signals

A novel Bayesian approach to detection-estimation of complex sinusoids and their frequencies is proposed. Based on Bayesian predictive densities, an objective function is derived whose minimization yields the optimal number of sinusoids and the estimates of their frequencies. This function is similar in form to the well known minimum description length (MDL) principle and Akaike´s information criteria (ALC) in the sense that it also consists of data and penalty terms. The minimization of the data term provides the frequency estimates, and the overall minimization yields the detected number of sinusoids. The simulation results show excellent performance.