TITLE:

PIECEWISE INTERPOLATION OF SINUSOID FUNCTIONS: A NEW PERSPECTIVE

DATE:

Friday, Oct 26th, 2012

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Ashkan Ashrafi.
Assistant Professor, Department of Electrical & Computer Engineering.
Adjunct Professor, Computational Science Research Center.
Member, Engineering Research Center for Sensorimotor Neural Engineering.
Director, Real-Time DSP and FPGA Development Laboratory.
San Diego State University.

ABSTRACT:

Piecewise polynomial interpolation of functions is a classic problem where the goal is
to minimize the error between the interpolating polynomials and the function being
approximated. The metric to measure the error is determined by a norm of the error function.
This could be a Euclidean norm (norm-2), Chebyshev norm (norm-infinity), norm-1 or any
other metric that evaluates the distance between the interpolating polynomials and the
function being approximated in the defined function space. In this framework, perhaps,
sinusoid functions are among the easiest functions to be approximated due to their well-
defined behavior. In this talk, we look at the problem from a different perspective. Instead
of approximating sinusoid functions in their defined domain, we approximate them in the
Fourier domain. A perfect sinusoid function has a non-zero fundamental harmonic and its other
harmonics are all zero. But all non-fundamental harmonics of the interpolated version of a
sinusoid are non-zero. We call these non-zero harmonics “spurs”. The goal is to find a piecewise
polynomial interpolation scheme that minimizes the maximum magnitude of the spurs. The
result of this interpolation is counterintuitive, i.e. it does not coincide with the optimum
approximation in the function’s original domain. For example, solution of this problem will
result in a discontinuous function. This problem and its solution have applications in designing
Direct Digital Frequency Synthesizers which will also be discussed in this talk.

HOST:

Dr. Sunil Kumar.

DOWNLOAD: