A Review of Maximum Entropy Spectral Analysis and Applications to Fourier Spectroscopy.
AIR FORCE GEOPHYSICS LAB HANSCOM AFB MA
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There are many situations where a great increase in the resolution of power spectral densities, PSDs, would solve important problems. The problem areas range from radar, speech compression, seismic signal processing, to spectral analysis of optical signals. The maximum entropy method MEM can, under certain circumstances, provide an order of magnitude increase in resolution over conventional techniques. The fundamental concepts and mathematical background are given and, most importantly, the peculiarities and new features introduced by the MEM technique are explained. Some signals are good candidates for this technique while others are not thus, methods are described to distinguish between the two. After the techniques to obtain the MEM-PSD are explained, an application to Fourier Spectroscopy is given to illustrate the results as compared to conventional means. This review employs certain features to make the MEM approach accessible to those without previous knowledge about it. These features include a short history of the PSD which describes the evolution over time of the basic concepts a discussion of the higher principle of maximum entropy in the context of probability theory a simple introduction to the Z-transform and how it introduces the basic spectral line shape of the MEM-PSD as well as other peculiarities of the method which distinguish it from the conventional approach the physics behind the reflection coefficients which are introduced by MEM and an extensive annotated bibliography which should make the literature available.
- Statistics and Probability