NDLI: Near orthogonal discrete quaternion Fourier transform components via an optimal frequency rescaling approach

Content Provider	IET Digital Library
Author	Hu, Lingyue Ling, Bingo Wing Kuen Ho, Charlotte Yuk Fan Huang, Guoheng
Abstract	The quaternion-valued signals consist of four signal components. The discrete quaternion Fourier transform is to map these four signal components in the time domain to that in the frequency domain. These four signal components in the frequency domain are called the discrete quaternion Fourier transform components. There are a total of 16 inner products among any two discrete quaternion Fourier transform components. The total orthogonal error among the discrete quaternion Fourier transform components is defined based on these 16 inner products. This study aims to find the optimal quaternion number in the discrete quaternion Fourier transforms so that the total orthogonal errors among the discrete quaternion Fourier transform components are minimised. It is worth noting that finding the optimal quaternion number in the discrete quaternion Fourier transform is equivalent to finding the optimal rescaling factors. Since the discrete quaternion Fourier transform components are expressed in terms of the high-order polynomials of the trigonometric functions of the rescaling factors, this optimisation problem is non-convex. To address this problem, a two-stage approach is employed for finding the solution to the optimisation problem. The comparison results show that the authors proposed method outperforms the existing methods in terms of achieving the low total orthogonal error among the discrete quaternion Fourier transform components.
Starting Page	634
Ending Page	642
Page Count	9
ISSN	17519675
Volume Number	14
e-ISSN	17519683
Issue Number	Issue 9, Dec (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/14/9
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2020.0199
Journal	IET Signal Processing
Publisher Date	2020-08-24
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Discrete Fourier Transform High-order Polynomials Integral Transforms Minimisation Near Orthogonal Discrete Quaternion Fourier Transform Component Optimal Frequency Rescaling Optimal Quaternion Number Optimisation Technique Polynomial Quaternion-valued Signal Signal Component Signal Processing Signal Processing And Detection Signal Processing Theory Trigonometric Function
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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