The Padé-Prony Method
Another variation of Prony's method, described by Burrus and Parks  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 .
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.