Formant Extraction Algorithm Using LSP Analysis

LSP analysis is a widely used technique in speech signal processing, particularly advantageous for formant extraction. This algorithm leverages the frequency-domain representation of Linear Predictive Coding (LPC) by transforming parameters into the Line Spectrum Pair (LSP) domain to achieve more stable formant estimation results. The core algorithmic approach treats speech signals as an all-pole model, first performing LPC analysis to obtain prediction coefficients, then converting these coefficients into LSP parameters. LSP parameters exhibit excellent quantization properties, with their zero positions directly corresponding to formant frequencies in speech signals. Compared to direct LPC domain processing, LSP analysis provides more intuitive frequency-domain interpretation and superior numerical stability. In practical implementation, the algorithm processes these key steps: preprocessing and framing of input speech signals; computing autocorrelation coefficients for each frame; solving LPC coefficients through Levinson-Durbin recursion; converting LPC polynomials to LSP polynomials; obtaining LSP frequencies through root-solving operations; and finally identifying and tracking formants based on LSP frequency distribution. Code implementation typically involves functions for frame segmentation, autocorrelation calculation, Levinson-Durbin algorithm, and root-finding methods for polynomial solutions. Compared to traditional peak-picking techniques, this method more accurately separates adjacent formants, demonstrating particularly stable performance in high-frequency regions. Additionally, the quantization characteristics of LSP parameters make them ideal for speech coding and synthesis applications, establishing a unified framework for both analysis and synthesis components. The algorithm's robustness is often enhanced through formant tracking algorithms that employ dynamic programming or Hidden Markov Models for temporal continuity.