Prony's method

Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer. Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids. This allows for the estimation of frequency, amplitude, phase and damping components of a signal. Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer. Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex exponentials or sinusoids. This allows for the estimation of frequency, amplitude, phase and damping components of a signal. Let f ( t ) {displaystyle f(t)} be a signal consisting of N {displaystyle N} evenly spaced samples. Prony's method fits a function to the observed f ( t ) {displaystyle f(t)} . After some manipulation utilizing Euler's formula, the following result is obtained. This allows more direct computation of terms.