/en/tags/fdaf/Recent content in FDAF on Mi&Bee BlogHugo -- gohugo.ioen蓝宝石的傻话Thu, 14 May 2026 10:00:00 +0800/en/posts/physical-world/variable-step-frequency-domain/Thu, 14 May 2026 10:00:00 +0800/en/posts/physical-world/variable-step-frequency-domain/<h2 id="the-convergence-trade-off-of-fixed-step-size">The Convergence Trade-off of Fixed Step Size</h2> <p>Standard LMS and NLMS algorithms use a fixed step size parameter $\mu$. The choice of step size directly impacts algorithm performance, but a fundamental contradiction exists:</p> <ul> <li><strong>Large step size</strong>: Fast convergence and quick adaptation to environmental changes, but large steady-state error and low filtering precision</li> <li><strong>Small step size</strong>: Small steady-state error and high filtering precision, but slow convergence and sluggish response to abrupt changes</li> </ul> <p>This contradiction is particularly pronounced in applications such as echo cancellation and active noise control — the system needs fast convergence during startup, yet wishes to maintain low error in steady state. A fixed step size cannot satisfy both phases simultaneously.</p>