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Series expansion for functions bandlimited to a ball.(Technical report)
- Article from:
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Sampling Theory in Signal and Image Processing
- Article date:
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January 1, 2008
- Author:
- Campbell, L. Lorne
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Copyright informationCOPYRIGHT 2008 Sampling Publishing. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract
An expansion related to the sampling theorem is derived for functions with Fourier transforms that vanish outside a ball in d dimensions. Such functions are determined by weighted averages of their values on a sequence of spheres in [R.sup.d]. The number of measurements per unit volume is equal to the Nyquist-Landau density. Fourier transforms that vanish outside ellipsoids and outside Cartesian products of balls are also considered.
Key words and phrases: Nyquist-Landau density, Nyquist rate, multidimensional sampling theorems, bandlimited functions
1 Introduction
The Nyquist rate is one of the fundamental constraints on the processing of ...
<[e.sup.-i2[pi]x x y], [[psi].sub.kmn](y)><[P.sub.KN](y), [e.sup.-i2[pi]x x y]>