A novel technique to design optimum FIR digital filters with different transition bandwidths

An efficient technique to reduce the impact of extraneous peaks in the transition bands of optimum FIR filters with three or more bands is presented. Currently, these filters are designed with an assumption of transition bands as “don´t care” regions. This assumption works perfectly until all the transition bandwidths are equal. If this is not the case, the phenomenon of extraneous peaks in the transition bands of the filter may occur. In theoretical designs, any performance in transition bands is acceptable, but in practice, resonances are not acceptable and may have adverse consequences on the overall design and application. This article reformulates the filter design approximation problem by employing certain transition band constraints in such a way that the phenomenon of extraneous peaks is reduced to an acceptable limit. Furthermore, an efficient MATLAB based implementation of the Remez algorithm is employed to obtain the filters without undesired transition band peaks. Several examples are included to highlight the efficiency of the proposed approach.