This　article　offers　a　detailed　exploration　of　the　Normalized　Least　Mean　Squares　(NLMS)　algorithm,　highlighting　its　enhanced　adaptive　filtering　capabilities　and　robust　performance　in　managing　input　signal　correlations.　It　delves　into　the　foundational　principles　of　the　NLMS　algorithm　and　outlines　the　essential　modules　required　for　its　implementation　in　Verilog　HDL.　The　implementation　and　simulation　of　the　NLMS　adaptive　filter　are　studied.　The　simulation　outcomes　indicate　that　the　convergence　rate　of　the　algorithm　is　superior　to　that　of　the　conventional　LMS　algorithm.　©　2025　Institute　of　Physics　Publishing.　All　rights　reserved.