Stagger-period sequences are a kind of discrete-time
sequences, but the Fourier analysis of the uniform-period, discrete-time
sequences does not apply to a stagger-period sequence; this means that the
uniform-period analytical conclusions would be misleading. In this chapter we
first define the essential concepts related to the stagger-period sequence and
the stagger-lag autocorrelation matrix; we propose the Fourier transform pair
of the stagger-period deterministic sequence and its spectrum, and discuss properties
related to the transform pair, such as the orthogonality of a complex staggered
exponential sequence, extension of the spectral period, Toeplitz of the
circularly stagger-lag matrix, the staggered Parseval’s theorem, etc.; we
verify inverses of each other of this transform pair and derive the convergence
condition of this Fourier transform. Then, another Fourier transform pair of
the stagger-lag autocorrelation matrix and its power spectrum density,
properties related to this transform pair, inverses of each other of this
transform pair, and the convergence condition of this Fourier transform of
power spectrum are also studied. During illustrating examples, the similarities
and differences of the equations and properties between the uniform-period and
stagger-period analyses are described. Two applications of the Fourier
analysis: search of the best stagger periods and spectrum estimation of the
stagger-period sequence, are also discussed in details later. In the end, the
advantages and methodologies of this study are summarized. This chapter “The
Fourier Analysis for Stagger-Period Sequences, its Applications” will open the
first page of the stagger-period signal processing.
Author(s) Details:
Xubao Zhang,
Electrical & Electronic Department, Xi’an Electronic Science and
Technology University, China.
Please see the link here: https://stm.bookpi.org/CPPSR-V7/article/view/13446
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