Fourier Analyses of Stagger-Period Sequences**

Abstract

Stagger-period sequences are a kind of temporal sequences, but Fourier analysis for a uniform-period sequence is not available to a stagger-period sequence; it means that the analytic conclusions would be misleading. We first define essential concepts related to a stagger-period sequence and a stagger-lag autocorrelation matrix, and propose a Fourier transform pair of a staggerperiod deterministic sequence and its spectrum; we analyze properties related to this transform pair, such as the orthogonality of a complex exponential sequence, spectral periodic extension, Toeplitz of circularly stagger-lag matrix and the staggered Paseval’s theorem, etc.; we verify inverses of each other of this pair, and derives a convergence condition of the transform. Then, another Fourier transform pair of a stagger-lag autocorrelation matrix and its power spectrum density, properties related to this pair, inverses of each other of this pair and a convergence condition of the transform, in this paper, are also studied. During analyzing, the similarities and differences between the uniform-period and stagger-period counterparts are discussed. Two applications of these Fourier analyses, search of optimal stagger periods and spectrum estimation of stagger-period sequences, are also described in details. In the end, the advantages and methodology of this study are summarized.