Correlation function for the weight sequence of the frequency domain adaptive filter

The statistical behavior of the single complex adaptive weight in the frequency domain adaptive filter is further investigated. In a previous note [8], an expression was evaluated for the expected value of the magnitude square of the weight sequence at any time. In this note, the covariance of the weight at different times is evaluated and, in steady state, shown to be geometric with the same time constant as the frequency domain adaptive filter algorithm itself. Using these results, the reduction in the fluctuations of the weight values are computed for an exponentially decaying post-algorithm filter.