# Frequency Tracking: LMS and RLS Applied to Speech Formant Estimation (2000)

## TL;DR

This paper explores adaptive filtering algorithms, LMS and RLS, for estimating speech formant frequencies, addressing the limitations of stationarity assumptions in speech processing.

## Contribution

It applies and compares LMS and RLS adaptive algorithms to speech formant estimation, a novel approach for dynamic speech analysis.

## Key findings

- LMS and RLS algorithms effectively track formant frequencies.
- RLS provides faster convergence than LMS.
- Adaptive methods outperform static estimation techniques.

## Abstract

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

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Source: https://tomesphere.com/paper/1812.02705