Approximation of [OMEGA]-bandlimited functions by [OMEGA]-bandlimited trigonometric polynomials.(Report) Sampling Theory in Signal and Image Processing | September 1, 2007| | COPYRIGHT 2007 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) Copyright

Abstract

It is known that the space of [OMEGA]-bandlimited functions is dense in [L.sup.2] norm on any finite interval [a, b]. In particular, for any [OMEGA] > 0 there exist so-called superoscillating [OMEGA]-bandlimited functions which can oscillate arbitrarily quickly on any finite interval of arbitrary length. This raises the question, is any [OMEGA]-bandlimited function in some sense the limit of a sequence of [OMEGA]-bandlimited trigonometric polynomials whose periods become infinite in length? Although the existence of superoscillating bandlimited functions ...

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