Extraction of LPC, LPCC, and MFCC Coefficients for a Vowel and an Unvoiced Consonant with Spectral Analysis

This document describes a comprehensive MATLAB-based analysis of speech signal processing techniques for phonetic characterization. First, we will implement feature extraction for one vowel and one unvoiced consonant using MATLAB. The implementation will include Linear Predictive Coding (LPC) coefficients, LPC Cepstral Coefficients (LPCC), and Mel-Frequency Cepstral Coefficients (MFCC). For LPC and LPCC extraction, we specifically employ the autocorrelation method using MATLAB's `lpc()` function, which solves the Yule-Walker equations through Levinson-Durbin recursion. The MFCC extraction will involve frame blocking, Hamming windowing, FFT computation, Mel-filter bank application, and discrete cosine transform, typically implemented using MATLAB's `mfcc()` function or custom implementations. Next, we will perform power spectrum estimation using LPC analysis for both speech signals. We will compute LPC spectra using four different model orders: 5th, 10th, 15th, and 20th-order. The implementation involves calculating the LPC transfer function magnitude response using `freqz()` in MATLAB. We will create a comparative plot displaying the original signal's FFT power spectrum alongside the four LPC spectral estimates, allowing for analysis of how model order affects spectral resolution and smoothing characteristics. Finally, we will implement the log area ratio method to generate variable cross-section vocal tract simulations for both pronunciations. Using 10th-order LPC coefficients obtained through the autocorrelation method, we will convert reflection coefficients to area ratios and plot the vocal tract area function. This simulation helps visualize sound propagation and transformation through the vocal tract, implemented using MATLAB's conversion functions between LPC coefficients and reflection coefficients. These modifications and additions provide comprehensive technical details while maintaining the original document's core objectives, making the content suitable for international technical documentation and research applications.