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The sampling theory is basic and crucial in engineering sciences. On the other hand, the linear canonical transform (LCT) is also of great power in optics, filter design, radar system analysis and pattern recognition, etc. The Fourier transform (FT), the fractional Fourier transform (FRFT), Fresnel transform (FRT) and scaling operations are considered as(More)
Collaborative representation-based classification (CRC) and sparse RC (SRC) have recently achieved great success in face recognition (FR). Previous CRC and SRC are originally designed in the real setting for grayscale image-based FR. They separately represent the color channels of a query color image and ignore the structural correlation information among(More)
and Applied Analysis 3 on each of the components of the distribution. We will use the following results: 1̂ (ω 1 , ω 2 ) = (2π) 2 δ (ω 1 , ω 2 ) , (14) ̂ (i−|α|Dαδ) (ω 1 , ω 2 ) = ω α1 1 ω α2 2 , (15) where α = (α 1 , α 2 ), |α| = α 1 + α 2 , D = (∂/∂x 1 ) α1 (∂/∂x 2 ) α2 , and δ is the usual Dirac delta function. In the following we introduce the LCT for(More)
In this paper, we study the optimal control problem for a class of four dimensional linear systems based on quaternionic and Fourier analysis. When the control is unconstrained, the optimal ensemble controller for this linear ensemble control systems is given in terms of prolate spheroidal wave functions (PSWFs). For the constrained convex optimization(More)
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(More)
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields(More)