Implementation of Time-Domain Adaptive Filtering Using QR Decomposition-Based Recursive Least Squares Algorithm

This document explores the implementation methodology of a time-domain adaptive filtering algorithm based on QR decomposition for recursive least squares estimation. This algorithm represents an advanced digital signal processing technique applicable across multiple domains including audio signal processing, image processing, and communication systems. The fundamental principle involves using QR decomposition and recursive least squares methods to estimate signal errors, while employing adaptive filters to reduce noise and enhance signal quality. Specifically, the algorithm recursively computes filter coefficients through sequential updates, enabling dynamic adaptation to signal variations. From an implementation perspective, key operations include: maintaining a QR-factorized covariance matrix for numerical stability, implementing Givens rotations for efficient matrix updates, and calculating weight vectors using back-substitution. This approach has demonstrated practical effectiveness by delivering superior signal quality and enhanced robustness, particularly in real-time processing scenarios where computational efficiency and numerical stability are critical. The recursive nature allows for O(n^2) computational complexity per iteration rather than O(n^3) for batch processing methods.