Frequency-domain implementations of periodically time-varying filters

Cyclostationary random processes have statistics that vary periodically in time. Optimum filtering of cyclostationary signals requires a filter whose impulse response also varies periodically in time. This paper describes computationally efficient methods for implementing periodically time-varying filters in the frequency domain. Both fixed and adaptive filtering is discussed. Two frequency-domain approaches are considered-overlap-save and transmultiplexer. A transmultiplexer is an efficient way of implementing a bank of bandpass filters. The overlap-save technique is found to be slightly more efficient than the transmultiplexer approach for fixed filters. For adaptive filtering, however, the transmultiplexer approach has an advantage over the overlap-save technique because the transmultiplexer allows the filter weights associated with each frequency to be adapted independently of weights for other frequencies.