Stronger uncertainty principles for hypercomplex signals

Abstract

In this paper, for real para-vector-valued signals, we obtain stronger uncertainty principles in terms of covariance and absolute covariance based on Fourier transform in both directional and the spatial cases. We provide certain conditions that give rise to the equal relation between the two uncertainty principles. Examples are presented to verify the results.

Keywords:

• uncertainty principle in higher dimensions
• Fourier transform
• covariance

AMS Subject Classifications:

• 46F10
• 30G35

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Macao Science and Technology Development Fund, MSAR. Ref. 018/2014/A1; Macao Government FDCT 098/2012/A3; and University of Macau Multi-Year Research [grant number (MYRG) MYRG116(Y1-L3)-FST13-QT].