A simplified variable step-size LMS algorithm for Fourier analysis and its statistical properties

• A simplified VSS-LMS (SVSS-LMS) algorithm is proposed for Fourier analysis.
• Its performance is comparable to most of the seven typical VSS-LMS algorithms.
• In-depth performance analysis is provided for the proposed algorithm.
• Simulations are conducted to confirm the performance and the analytical results.

In this paper, several typical variable step-size LMS (VSS-LMS) algorithms are first applied to adaptive Fourier analysis of noisy sinusoidal signals, which were developed in the context of system identification. A simplified VSS-LMS (SVSS-LMS) algorithm is then proposed to perform the same task, which, on the whole, indicates nice performance comparable to that of most of the typical VSS-LMS algorithms, and requires fewer multiplications as well as user parameters. In-depth performance analysis is provided for the proposed algorithm. Difference equations are derived that describe its dynamics, and elegant closed-form expressions are also worked out for its steady-state performance. Extensive simulations are conducted to confirm its effectiveness, and to clarify the validity of the analytical findings.