Application of infinite dimensional linear programming to FIR filter design with time domain constraints

Previously the envelope-constrained filtering problem was formulated as designing an FIR filter such that the filter´s L₂ norm is minimised subject to the constraint that its response to a specified input pulse lies within a prescribed envelope. We recast this filter design problem as a frequency-domain L_∞ optimization problem with time-domain constraints. Motivations for solving this problem are given. Then infinite dimensional linear programming techniques are used for the design of the required FIR filter. For illustration, we apply the approach to a numerical example which deals with the design of an equalization filter for a digital transmission channel