Comparing a Complex-Valued Sinusoidal Process with an Autoregressive Process Using Jeffrey’s Divergence

This paper deals with the analysis of the Jeffrey's divergence (JD) between an autoregressive process (AR) and a sum of complex exponentials (SCE), whose magnitudes are Gaussian random values, which is then disturbed by an additive white noise. As interpreting the value of the JD may not be necessarily an easy task, we propose to give an expression of the JD and to analyze the influence of each process parameter on it. More particularly, we show that the ratios between the variance of the additive white noise and the variance of the AR-process driving process on the one hand, and the sum of the ratios between the SCE process power and the AR-process PSD at the normalized angular frequencies on the other hand, has a strong impact on the JD. The 2-norm of the AR-parameter has also an influence. Illustrations confirm the theoretical part.