An Investigation of Discrete Sampling from a Phase-Space Perspective

Bryan Hennelly

CS, National University of Ireland, Maynooth


Whittaker, Nyquist, Kotelnikov and Shannon developed the sampling theory and interpolation formula for bandlimited signals over fifty years ago. Their theories show how a continuous function, with a Fourier Transform of finite width, can be completely reconstructed from its discrete sample values if it is sampled at a sufficient uniform rate. We interpret sampling theory using the Wigner Distribution Function, time-frequency or phase-space description often encountered in signal processing, optics and quantum mechanics. We show how this interpretation offers significant insight into sampling and interpolation. In particular we discuss the sampling of signals that have a variable local bandwidth, implying that in certain places the signal varies rapidly while in others it varies more slowly. The subject of non-uniform sampling, in which the sampling rate changes in correspondence with the local bandwidth, has been an active of research for over two decades and has application in many areas of science. We believe that the Wigner interpretation offers new insight into the optimum non-uniform sampling distribution and interpolation formula for particular signals.

Biography

Bryan Hennelly received his BE in Electronic Engineering from University College Dublin (UCD), Ireland in 2001. He was awarded his PhD, also from UCD, in optical engineering three years later having made contributions to three separate areas of optical science; optical metrology, optical encryption and the development of fast algorithms for use in optical signal processing. Having spent a number of years lecturing, he is currently a postdoctoral researcher in the National University of Ireland, Maynooth and is a fellow of the Irish Research Council for Science, Engineering and Technology. At present he conducts research in digital holography, 3-D image recording and 3-D optical displays.

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