Bayesian model order determination rule for harmonic signals

The model order selection in signal processing problems has often been addressed by employing the Akaike information criterion (AIC) and the minimum description length principle (MDL). The popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented. They can, however, produce misleading results if they are indiscriminately utilized. A case in point is the problem of model order selection of sinusoidal signals embedded in Gaussian noise. Following the Bayesian methodology, for these signals we derive the Bayesian methodology, for these signals we derive a model order selection criterion whose general form is similar to the AIC and MDL. It contains both, the log-likelihood and the penalty terms, the latter of which is modified and more appropriate for the selection of sinusoidal signals. Simulation results are provided, and they disclose remarkable improvement in our selection rule over the MDL and AIC.