Optimal Quantizer Based on Lloyd-Max Algorithm

This document presents an optimal quantizer program based on the Lloyd-Max algorithm, where lloydmax serves as the main program. The Lloyd-Max algorithm is a clustering method widely used in signal processing and image applications, designed to partition n data points into k distinct categories while minimizing inter-cluster variance. The core algorithm operates through iterative centroid updates - repeatedly recalculating cluster centers based on current assignments until convergence criteria are met. The quantizer implementation handles critical operations including probability density function estimation, quantization level initialization, and distortion measurement through multiple iterations. This quantizer program finds applications across various domains such as image compression and signal encoding, making it a valuable tool that plays significant roles in modern technological applications. The code typically involves functions for threshold calculation, centroid optimization, and convergence checking to ensure optimal quantization performance.