Title/Authors
Filter design under magnitude constraints is a finite dimensional convex
optimization problem
L. Rossignol, G. Scorletti and V. Fromion
Abstract
We consider the design of filters satisfying upper and lower bounds on
the frequency response
magnitude, in the continuous and discrete time domains. The paper contribution
is to
prove that such a problem is equivalent to a finite dimensional convex
optimization program
involving Linear Matrix Inequality contraints. At now, such optimization
problems
can be efficiently solved. Note that this filter design problem is
usually reduced to a
semi infinite dimensional Linear Programming optimization problem under
the additional
assumption that the filter poles are fixed (for instance, when considering
FIR design).
Furthermore, the semi infinite dimensional optimization is practically
solved, using a gridding
approach on the frequency. In addition to be finite dimensional, our
formulation allows to
set or not the filter poles. Numerical applications emphasize the interest
of the proposed results.
Status
Published In 40th IEEE Conference on Decision and Control, pages 3575-3580,
Orlando, Florida USA, December 2001. accepted to IJNRC, 2003.
Download