Which mathematical procedure is used for extracting formant frequencies?

The extraction of formant frequencies, which are the resonant frequencies of the vocal tract that characterize the quality of vowel sounds, is most effectively performed using Linear Predictive Coding (LPC). LPC analyzes the speech signal by modeling it as a linear combination of previous samples. This method estimates the formant frequencies by determining the coefficients of the filter that best approximates the speech waveform, allowing for an efficient representation of the spectral envelope, which in turn identifies the formants.

While all the methods mentioned can analyze speech signals, LPC is particularly designed for formant extraction due to its ability to provide a compact representation and focus on the resonant features of the vocal tract. It accomplishes this by minimizing the mean square error between the actual speech signal and the predicted signal based on past samples, which leads to accurate identification of the formants.

Fourier Transform, while useful for analyzing frequency components of a signal, does not efficiently isolate the formants from the rest of the acoustic signal. Wavelet Analysis also provides time-frequency analysis but is not specifically tailored for formant extraction in speech. Statistical Analysis could be employed in various contexts but does not directly pertain to the extraction of phonetic features like formant frequencies in speech signals. Hence, LPC is