Yang+Kou: Uncertainty principles for hypercomplex signals in the linear canonical transform domains


Yan Yang, Kit Ian Kou, Uncertainty principles for hypercomplex signals in the linear canonical transform domains, Signal Processing, Volume 95, February 2014, Pages 67–75. DOI: 10.1016/j.sigpro.2013.08.008

Abstract
Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. In this paper, we extend the uncertainty principle for hypercomplex signals in the linear canonical transform domains, giving the tighter lower bound on the product of the effective widths of complex paravector- (multivector-)valued signals in the time and frequency domains. It is seen that this lower bound can be achieved by a Gaussian signal. An example is given to verify the result.

Keywords: Linear canonical transform, Uncertainty principle, Hypercomplex signals, Gaussian signals

Source: http://www.sciencedirect.com/science/article/pii/S0165168413003186, Email by Kit Ian Kou, kikou_AT_umac.mo 30 Oct. 2013

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