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.