### The Padé-Prony Method

Another variation of Prony's method, described by Burrus and Parks
[9] consists of using *Padé* approximation to
find the numerator
after the denominator
has been found
as before. Thus,
is found by matching the first
samples of , *viz.*,
. This method is faster, but does not generally give
as good results as the previous version. In particular, the degenerate
example
gives
here as did pure
equation error. This method has been applied also in the stochastic
case [11].

On the whole, when is causal and minimum phase (the ideal situation for just about any stable filter-design method), the variants on equation-error minimization described in this section perform very similarly. They are all quite fast, relative to algorithms which iteratively minimize output error, and the equation-error method based on the FFT above is generally fastest.

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Method

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Prony's Method