A MODEL SELECTION RULE FOR SINUSOIDS IN WHITE GAUSSIAN-NOISE

The model selection problem for sinusoidal signals has often been addr essed by employing the Akaike information criterion (AIC) and the mini mum description length principle (MDL), The popularity of these criter ia partly stems from the intrinsically simple means by which they can be implemented, They can, however, produce misleading results if they are not carefully used, The AIC and MDL have a common form in that the y comprise two terms, a data term and a penalty term, The data term qu antifies the residuals of the model, and the penalty term reflects the desideratum of parsimony, While the data terms of the AIC and MDL are identical, the penalty terms are different, In most of the literature , the AIC and MDL penalties are, however, both obtained by apportionin g an equal weight to each additional unknown parameter, be it phase, a mplitude, or frequency, By contrast, in this paper, we demonstrate tha t the penalties associated with the amplitude and phase parameters sho uld be weighted differently than the penalty attached to the frequenci es, Following the Bayesian methodology, we derive a model selection cr iterion for sinusoidal signals in Gaussian noise which also contains t he log-likelihood and the penalty terms, The simulation results disclo se remarkable improvement in our selection rule over the commonly used MDL and AIC.