The rate of convergence of the parameters of adaptive filters with quasi-harmonic input signals

A theoretical study of the rate of convergence of the parameters (the weighting coefficients) of adaptive filters with quasi-harmonic input signals is presented. The analysis is based on the solution of the stochastic equation for the weighting coefficients without the use of a time-averaging procedure. Conditions under which a reduction occurs in the rate of convergence are determined; these conditions are described by a specific relationship for input-signal power, the gain and time constant of the filter in the feedback circuit, and the carrier frequency of the sinusoidal signal. It is noted that the present results are valid also for adaptive antenna arrays with compensation of narrow-band noise.