Maximum entropy spectral analysis of multiple sinusoids in noise

An analytical technique based on the method of undetermined coefficients is applied to the problem of computing the theoretical spectral estimate by the maximum entropy method (MEM) when the autocorrelation function of the data is known exactly and corresponds to N sinusoids in additive white noise and to N sinusoids in additive l-pole, low-pass noise. For the white noise case, the L prediction filter coefficients are expanded directly in terms of the input sinusoids. This expansion leads to a transformation of the L x L normal equations for the prediction filter coefficients to a set of 2N x 2N equations. The transformed equations are a smaller set of equations to be solved whenever L > 2N and provide a convenient description of the interaction between the various frequency components of the sinusoids which occurs in the MEM estimate. Further. for certain cases where there is little interaction between some of the fre-