The n-D analytic signals and Fourier spectra in complex and hypercomplex domains

K. Snopek
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引用次数: 3

Abstract

In the paper, two various representations of a n-D real signal are investigated. The first one is the n-D complex analytic signal with a single-orthant spectrum defined as the extension of the 1-D Gabor's analytic signal. The second one is the n-D hypercomplex analytic signal defined in Clifford and Cayley-Dickson algebras. Their signal-domain and frequency-domain definitions are presented and compared. Some relations between the spectra in 2-D and 3-D hypercomplex domains are presented. The paper is illustrated with the example of a 2-D separable Cauchy pulse.
复域和超复域的n-D解析信号和傅立叶谱
本文研究了n-D实信号的两种不同表示形式。第一类是n-D复解析信号,其单正交谱定义为一维Gabor解析信号的扩展。第二种是定义在Clifford和Cayley-Dickson代数中的n-D超复解析信号。给出并比较了它们的信号域和频域定义。给出了二维和三维超复域光谱之间的一些关系。本文以二维可分离柯西脉冲为例进行了说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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