Frequency-response-shaped LMS adaptive filter

A new LMS algorithm is introduced for improved performance when a sinusoidal input signal is corrupted by correlated noise. The algorithm is based on shaping the frequency response of the transversal filter. This shaping is performed on-line by the inclusion of an additional term similar to the leakage factor in the adaptation equation of leaky LMS. This new term, which involves the multiplication of the filter coefficient vector by a matrix, is calculated in an efficient manner using the FFT. The proposed adaptive filter is shown analytically to converge in the mean and mean-square sense. The filter is also analyzed in the steady state in order to show the frequency-response-shaping capability. Simulation results illustrate that the performance of the frequency-response-shaped LMS (FRS-LMS) algorithm is very effective even for highly correlated noise.