On spectral theory of cyclostationary signals in multirate systems

This paper studies two problems in the spectral theory of discrete-time cyclostationary signals: the cyclospectrum representation and the cyclospectrum transformation by linear multirate systems. Four types of cyclospectra are presented, and their interrelationships are explored. In the literature, the problem of cyclospectrum transformation by linear systems was investigated only for some specific configurations and was usually developed with inordinate complexities due to lack of a systematic approach. A general multirate system that encompasses most common systems-linear time-invariant systems and linear periodically time-varying systems-is proposed as the unifying framework; more importantly, it also includes many configurations that have not been investigated before, e.g., fractional sample-rate changers with cyclostationary inputs. The blocking technique provides a systematic solution as it associates a multirate system with an equivalent linear time-invariant system and cyclostationary signals with stationary signals; thus, the original problem is elegantly converted into a relatively simple one, which is solved in the form of matrix multiplication.