The Prony Method and Its Application to Speech Analysis

Extraction of formant frequencies and bandwidths corresponds to extracting a best estimate (in the sense of ]east squares) of three or four exponentially damped sinusoids from an acoustic signal that contains these terms plus noise (e.g., glottal wave characteristics). Least‐square optimal estimation of the formant parameters is a nonlinear problem and must be solved iteratively, as in the “Analysis‐by‐Synthesis” methods. Prony's method, originally formulated in 1795, is now becoming recognized as a very powerful method of obtaining near‐optimal formant parameter estimates without iteration. The algorithms required in the Prony method are reviewed along with results from different applications. It is shown that, in many instances, formant parameter and pitch extraction comparable in quality to cepstral techniques can be obtained over the full range of male voices to children's voices. In practice, the method appears to have a convergence property in which the use of more terms leads to more accurate forma...