CARMA COLLOQUIUM Speaker: A/Prof. Jeff Hogan, CARMA, The University of Newcastle Title: Prolate spheroidal wavefunctions and the "lucky accident" Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 5th Aug 2010 Abstract: The classical prolate spheroidal wavefunctions (prolates) arise when solving the Helmholtz equation by separation of variables in prolate spheroidal coordinates. They interpolate between Legendre polynomials and Hermite functions. In a beautiful series of papers published in the Bell Labs Technical Journal in the 1960's, they were rediscovered by Landau, Slepian and Pollak in connection with the spectral concentration problem. After years spent out of the limelight while wavelets drew the focus of mathematicians, physicists and electrical engineers, the popularity of the prolates has recently surged through their appearance in certain communication technologies. In this talk we discuss the remarkable properties of these functions, the lucky accident'' which enables their efficient computation, and give details of their role in the localised sampling of bandlimited signals. [Permanent link]