A fast windowing technique for designing discrete wavelet multitone transceivers exploiting spline functions

A very fast technique for designing discrete wavelet multitone (DWMT) transceivers without using time-consuming nonlinear optimization is introduced. In this method, the filters in both the transmitting and receiving filter banks are generated based on the use of a single linear-phase finite-impulse response prototype filter and a cosine-modulation scheme and the prototype filter is optimized by using the windowing technique. The novelty of the proposed technique lies in exploiting spline functions in the transition band of the ideal filter, instead of using the conventional brick-wall filter. In this approach, a simple line search is used for finding the passband edge of the ideal filter for minimizing a predetermined cost function. The resulting DWMT transceivers closely satisfy the perfect reconstruction property, as is illustrated by means of examples.