An explicit solution and data extension in the maximum entropy method

The Lagrange undetermined multiplier method and the cepstrum analysis method are used to determine an explicit solution and a data extension model in the maximum entropy method of power spectrum analysis. The 1-dimensional case for a real, causal, stable, and all-pole signal is treated. Only the definition of entropy as
H_{2} = -\int S(f) \log S(f) df
is treated although the same treatment has been applied to
H_{1} = \int \log S(f) df
. Relevant results of cepstrum analysis are provided. This paper concludes with a numerical example.