Continuous-time envelope-constrained filter design via Laguerre filters and ℋ∞ optimization methods

The envelope-constrained filtering problem is concerned with the design of a time-invariant filter to process a given input signal such that the noiseless output of the filter is guaranteed to lie within a specified output mask while minimizing the noise gain of the filter. An algorithm is developed to solve the continuous-time envelope-constrained filter design problem with the ℋ_∞ norm of the filter as the cost and an orthonormal set of basis filters. It is shown that the problem can be reformulated and solved as a constrained ℋ _∞ model-matching problem. To illustrate the effectiveness of the design method, two numerical examples are presented that deal with the design of equalization filters for digital transmission channels