Maximum Entropy Pole-Zero Estimation.
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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Maximum Entropy has been suggested by numerous authors as a good objective measure for optimally modeling the power spectrum of a wide-sense stationary random process. This documents describes a new Maximum Entropy pole-zero spectrum estimation method. The mathematical model is designed to achieve the maximum possible entropy subject to constraints on the first few correlation and cepstral values. The solution, which is in the form of an ARMA model, is based on solving a generalized, symmetric, almost-Toeplitz eigenvalue problem. The authors characterize the existence, uniqueness, stability and minimum phase properties of the solution, and categorize all possible occurrences of canceling pole-zero pairs. A search procedure based on a fast Levinson-like algorithm is given for estimating the model, and examples are presented ot illustrate its performance. A special case of the method gives a model estimate similar to that of Pisarenkos harmonic retrieval problem.
- Statistics and Probability