A dual approach to continuous-time envelope-constrained filter design via orthonormal filters

The envelope constrained (EC) filtering problem was initially posed in the continuous-time domain as a constrained L-2 space optimization problem. How ever, only the discretized version has been solved, using various approache s. In this paper me consider the continuous-time EC filtering problem formu lated using an orthonormal basis defined on a Hilbert vector space. Carathe odory's theorem and the dual parametrization method are used to obtain a du al finite-dimensional optimization problem, Two iterative algorithms based on the gradient flow technique are then developed for solving this dual pro blem. The design of an EC optimal equalization filter for a communication c hannel is solved to illustrate the effectiveness of the proposed algorithm.