Formant Estimation from Linear Prediction Spectra and Their Second Derivatives

Abstract

Merging of adjacent formants is probably the most common cause of failure to extract formants from smoothed spectra of typical voiced speech. Computation of spectra inside the unit circle is often used to resolve merged formants. This paper describes a method in which the second derivative of the smoothed spectrum is used to detect merged formants. Frequencies of the five largest peaks in the smoothed spectrum are measured. Frequencies of the five largest peaks in the second derivative of the spectrum are also measured. The frequencies of the two sets of five peaks are compared and second derivative peaks that duplicate spectral peaks are eliminated. The spectrum is considered to have unresolved peaks at the frequencies of the second derivative peaks which are not eliminated. The five highest amplitude peaks and/or unresolved peaks in the spectrum are considered to be the formants. The method has successfully resolved merged peaks in more than 80% of the cases tested. It is more efficient than computing spectra inside the unit circle, although probably somewhat less precise. Examples of speech spectra will be shown to illustrate the behavior of the method.