Fourier Transform Vs Prony/GPOF

[zinda_rud]

I have been recently reading papers on Generalized Pencil of Functions and Prony Method (parameteric modeling). It turns out that GPOF/Prony are very good in extracting resonances from a given data and don't suffer from the so called 'windowing effects' associated with FT.

My question is:

Is there any advantage of using FT (or specifically DFTs) in extracting poles/resonances from a given data or GPOF/Prony's are the best in all such cases?

Thanks.

 

[PaulDent]

If the number of poles is much lower than the number of data samples, a version of Prony would be suggested. Many improvements to Prony's algorithm have been made since 1795. The "smallest eigenvector" method of Howard J Price is better than Prony's original method. Still better is the optimum joint pole and coefficient estimation of Bresler and Macovski.
See D. Kundu's book "Computational aspects of statistical signal processing", chapter 14, which is on the web if you Google it.

 

[OptimalDesign]

... Is there any advantage of using FT (or specifically DFTs) in extracting poles/resonances from a given data or GPOF/Prony's are the best in all such cases?

'Windowing' causes FT and DFT problems that several http://www.digitalCalculus.com/demo/rainbow.html" don't have or at least don't show. Methods include Autocorrelation, Covariance, Prony, Akaike, Burg, etc. Steven Kay published a textbook about 1986 called 'modern spectral estimation' that convinced me to forget FT and start using these other methods. Prony was WAY ahead of his time it seems to me.