Statistical analysis for a variable step-size fourier analyzer

Fourier analyzer, based on variable step-size least mean square (LMS) algorithm, enjoys fast convergence, good tracking capability and small steady state errors. Thus, a thorough statistical analysis of the Fourier analyzer is of great significance. In this paper, differential equations governing the dynamic of the system are derived in the mean and mean square sense on the premise that the error signals obey Gauss distribution. Closed-form expressions indicating relationships of steady-state error, reference signal frequencies, system parameters and addictive noise are carried out for steady-state performance analysis, which can serve as the fundamental principle for system parameter selection. Numerous simulations confirm the validity of the analytical findings.