/en/tags/lms/Recent content in LMS on Mi&Bee BlogHugo -- gohugo.ioen蓝宝石的傻话Thu, 07 May 2026 10:00:00 +0800/en/posts/physical-world/adaptive-filtering-lms-nlms/Thu, 07 May 2026 10:00:00 +0800/en/posts/physical-world/adaptive-filtering-lms-nlms/<h2 id="the-lms-algorithm">The LMS Algorithm</h2> <p>The core problem in adaptive filtering is: given a reference signal <code>x(n)</code> and a desired signal <code>d(n)</code>, find a filter coefficient vector <code>w</code> such that the output <code>y(n)</code> approximates <code>d(n)</code>.</p> <p>The Least Mean Square (LMS) algorithm is the most classic solution to this problem, proposed by Widrow and Hoff in 1960. The core idea is to take one step down the steepest gradient of the error surface at each iteration — stochastic gradient descent.</p>