Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 beten 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.
['Kajetana M. Snopek']
I am writing a research paper on a idea The n-D analytic signals and Fourier spectra in complex and hypercomplex domains
[{"from": "human", "value": "I am writing a research paper on a idea The n-D analytic signals and Fourier spectra in complex and hypercomplex domains"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 beten 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."}]