CONTINUOUS-TIME ENVELOPE CONSTRAINED FILTER DESIGN VIA ORTHONORMAL FILTERS

The envelope constrained (EC) filtering problem is concerned with desi gning a filter which minimises the gain to input noise while its respo nse to a given signal fits into a prescribed envelope. This problem ha d been formulated as a constrained optimisation problem in Hilbert spa ce. By restricting these filters to the span of a finite orthonormal s et, the EC filtering problem can be posed as a finite-dimensional opti misation problem with a continuum of constraints. The constrained prob lem is approximated by an unconstrained problem which is then solved b y descent direction based algorithms. It is shown that these algorithm s converge globally, and one in particular has a quadratic rate of con vergence. Numerical examples using the orthonormal Laguerre series app roximation are studied.