Application of wavelets to envelope-constrained analog filter design for communication channel equalisation

The envelope-constrained filtering problem is concerned with the design of a time-invariant filter to process a given input pulse such that the output waveform of the filter is guaranteed to lie within a prescribed output mask. Using suitably chosen orthonormal wavelets, the envelope-constrained filter design problem has been reformulated and solved as an quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of wavelet series approximation offers a very simple and effective alterative to solving the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel