A new method for model order selection

The problem of recovering the continuous spectrum (noise spectrum) of a signal which is corrupted by a point spectrum is considered for the case where the signal consists of a countable number of sinusoids and the noise is stationary in a wide sense but unknown. A method for selecting model order
n
for the purpose of recovering the continuous spectrum is proposed. It is found that the spectrum oscillations for each order
n
occur at a frequency of approximately
n
Hz. This kernal viewpoint provides knowledge of the frequency of the oscillations as well as their magnitudes, which in turn suggests a number of methods for eliminating the oscillation in order to recover a continuous spectrum estimate. It is found that this oscillation phenomenon is another indication for the model order selection of an autoregressive filter. Two examples are included