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Model based signal processing or signal analysis or signal representation hasa rather different point of view from the more traditional filtering andalgorithm based approaches. However, in all of these, the names of Prony,Pad\'e, and linear prediction come up. This note examines these ideas with thegoal of showing they are all based on the same principles and all can beextended and generalized. A particular application is the frequency samplingdesign of IIR digital filters.

Prony, Pad\'e, and Linear Prediction for Interpolation and Approximation  in the Time and Frequency Domain Design of IIR Digital Filters and in  Parameter Identification