Frequency Tracking: LMS and RLS Applied to Speech Formant Estimation

1) Introduction Several speech processing algorithms assume the signal is stationary during short intervals (approximately 20 to 30 ms). This assumption is valid for several applications, but it is too restrictive in some contexts. This work investigates the application of adaptive signal processing to the problem of estimating the formant frequencies of speech. Two algorithms were implemented and tested. The first one is the conventional Least-Mean-Square (LMS) algorithm, and the second is the conventional Recursive Least-Squares (RLS) algorithm. The formant frequencies are the resonant frequencies of the vocal tract. The speech is the result of the convolution between the excitation and the vocal tract impulse response [Rabiner, 78], thus a kind of "deconvolution" is required to recover the formants. This is not an easy problem because one does not have the excitation signal available. There are several algorithms for formant estimation [Rabiner, 78], [Snell, 93], [Laprie, 94]. One popular scheme is to calculate an all-pole filter H(z) using the Linear Predictive Coding (LPC) technique based on Levinson-Durbin algorithm. The formants can be associated to the poles of H(z). The formants can be estimated through an adaptive algorithm as shown in [Hodgkiss, 81]. This work will present results for the conventional LMS and RLS algorithms.