James S. Walker, University of Wisconsin--Eau Claire, Eau Claire, WI 54702

    Modern, Computer Assisted, Fourier Analysis

During the past thirty years a revolution has occurred in applied Fourier
analysis.  The FFT algorithm has precipitated a synthesis of digital
computing and the classical techniques of Fourier analysis.  It is now
possible to teach fundamental methods of Fourier analysis, in an
interdisciplinary way, to undergraduates in physics, chemistry, computer
science, and mathematics.  Using computer graphics and the FFT algorithm,
one can easily display graphs of Fourier series, Fourier transforms,
interpolation series, and convolutions, and show how they are used to
solve problems in physics, signal processing, and optics. In physics, 
problems of heat conduction and vibration can be illustrated with an
increased emphasis on numerical results.  In signal processing, topics
such as noise removal, analog/digital conversion, and digital filtering
can be illustrated effectively with computer graphics.  And, in optics,
topics such as diffraction, imaging, and image processing provide a rich
field for interdisciplinary work.
    A summary will be given of the highlights of the author's work in
this area over the past twelve years.  Including a description of the
computer software (commercially published) which he has deveoloped to
teach this material.