Periods of interleaved and nonuniformly decimated sequences

Periods of interleaved and nonuniformly decimated integer sequences are analyzed. A characterization of the period of an interleaved sequence in terms of the constituent periodic integer sequences is first derived. This is then used to generalize the result of Blakley and Purdy (1981) on the period of a decimated integer sequence obtained by a periodic nonuniform decimation. The technique developed and results may be interesting for analyzing the period of various pseudorandom sequences, especially in stream cipher and spread-spectrum applications.