The Balian-Low Theorem for the Windowed Quaternionic Fourier Transform View Full Text


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Article Info

DATE

2012-12

AUTHORS

Yingxiong Fu, Uwe Kähler, Paula Cerejeiras

ABSTRACT

In this paper we present the Balian-Low theorem for the twosided windowed quaternionic Fourier transform (WQFT), a theorem which expresses the fact that time-frequency concentrations are incompatible with non-redundancy whenever Gabor systems form orthonormal bases or frames. Since uncertainty principles are closely connected with representations of the kernel of the Fourier transform under consideration, we construct a suitable representation for the kernel of our two-sided WQFT which in turn provides suitable Gabor systems. We proceed by deriving several important properties of the WQFT, such as shift and modulation operators, a reconstruction formula, orthogonality relations and a Heisenberg uncertainty principle for the WQFT. Finally, we establish the Balian-Low theorem for Gabor orthonormal bases associated with discrete versions of the kernels of the WQFT and of the right-sided WQFT. More... »

PAGES

1025-1040

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00006-012-0324-x

DOI

http://dx.doi.org/10.1007/s00006-012-0324-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1012314449


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