Frequency-domain and multirate adaptive filtering

An overview is presented of several frequency-domain adaptive filters that efficiently process discrete-time signals using block and multirate filtering techniques. These algorithms implement a linear convolution that is equivalent to a block time-domain adaptive filter, or they generate a circular convolution that is an approximation. Both approaches exploit the computational advantages of the FFT. Subband adaptive filtering is also briefly described. Here the input data are first processed by a bank of narrowband bandpass filters that are approximately nonoverlapping. The transformed signals are then decimated by a factor that depends on the degree of aliasing that can be tolerated, resulting in a large computational savings. Several performance issues are considered, including convergence properties and computational complexities of the adaptive algorithms and the effects of circular convolution and aliasing on the converged filter coefficients.<>