MATLAB Simulation of A-law PCM Encoding and Decoding in Speech Coding

This document explores the MATLAB simulation of A-law PCM encoding and decoding in speech coding systems. We provide a comprehensive explanation of the fundamental principles and procedural steps involved in A-law PCM encoding, accompanied by practical implementation examples to enhance understanding. The MATLAB simulation methodology is detailed with specific algorithmic approaches, including the implementation of compression characteristics using the A-law quantization formula: y = sign(x) * (A|x|)/(1+ln(A)) for |x| ≤ 1/A, and y = sign(x) * (1+ln(A|x|))/(1+ln(A)) for 1/A < |x| ≤ 1. Key MATLAB functions such as quantiz for quantization and compand for compression/expansion operations are discussed with implementation guidelines. The simulation framework demonstrates complete encoding-decoding chain verification through signal-to-noise ratio (SNR) calculations and waveform comparison techniques. Through this technical documentation, readers will acquire thorough knowledge of speech coding/decoding mechanisms and practical MATLAB simulation capabilities for real-world applications.