Pitt's inequality and the uncertainty principle associated with thc quaternion Fourier transform

UM > Faculty of Science and Technology > DEPARTMENT OF MATHEMATICS

Status	已發表Published
	Pitt's inequality and the uncertainty principle associated with thc quaternion Fourier transform
	Chen, C; Kou, K. I.; Liu, M.
	2015-03-01
Source Publication	Journal of mathematical analysis and applications
ISSN	0022-247X
Pages	681-700
Abstract	The quaternion Fourier transform – a generalized form of the classical Fourier transform – has been shown to be a powerful analyzing tool in image and signal processing. This paper investigates Pitt’s inequality and uncertainty principle associated with the two-sided quaternion Fourier transform. It is shown that by applying the symmetric form f = f1+if2+f3j+if4j of quaternion from Hitzer and the novel module or Lp-norm of the quaternion Fourier transform f , then any nonzero quaternion signal and its quaternion Fourier transform cannot both be highly concentrated. Two part results are provided, one part is Heisenberg–Weyl’s uncertainty principle associated with the quaternion Fourier transform. It is formulated by using logarithmic estimates which may be obtained from a sharp of Pitt’s inequality; the other part is the uncertainty principle of Donoho and Stark associated with the quaternion Fourier transform.
Keyword	Quaternion Fourier transform Pitt’s inequality Logarithmic uncertainty estimate Uncertainty principle
Language	英語English
The Source to Article	PB_Publication
PUB ID	14220
Document Type	Journal article
Collection	DEPARTMENT OF MATHEMATICS
Corresponding Author	Liu, M.
Recommended Citation GB/T 7714	Chen, C,Kou, K. I.,Liu, M.. Pitt's inequality and the uncertainty principle associated with thc quaternion Fourier transform[J]. Journal of mathematical analysis and applications, 2015, 681-700.
APA	Chen, C., Kou, K. I.., & Liu, M. (2015). Pitt's inequality and the uncertainty principle associated with thc quaternion Fourier transform. Journal of mathematical analysis and applications, 681-700.
MLA	Chen, C,et al."Pitt's inequality and the uncertainty principle associated with thc quaternion Fourier transform".Journal of mathematical analysis and applications (2015):681-700.

Files in This Item:
There are no files associated with this item.

If you have any objections to this item, please fill out the form below and the administrator will contact you as soon as possible.
Content:
Email：	*
Affiliation No.
Verification Code:	Refresh

Any comments and suggestions are welcomed.
Title:	*
Content:
Email：	*
Verification Code:	Refresh