A comparison of LMS adaptive cancellers implemented in the frequency domain and the time domain

Adaptive cancelling can be performed in the frequency domain with significant computational savings over time-domain implementations. This paper considers the statistical behavior of a frequency-domain adaptive canceller with white noise inputs, and develops expressions for the mean and variance of the adaptive filter weights, and for the mean-square error (MSE). These are compared to the behavior of a time-domain canceller with the same inputs through a combination of analysis and simulation. It is shown that the performance of the two algorithms can differ significantly due to the effects of block processing in the FFT. However, conditions are given under which the two implementations are essentially equivalent for white noise inputs so that the frequency-domain algorithm can be used to predict the mean, variance, time response, and MSE of the time-domain algorithm.