Design of linear phase FIR filters with uniformly flat band-response

A novel procedure that makes use of the maximum entropy method (MEM) for the design of linear-phase FIR (finite impulse response) digital filters is described. It is shown that, by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear-phase FIR filters that match the given gain function to any desired degree of accuracy. Moreover, an iterative algorithm makes the design procedure very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize the effect of any residual passband distortion, a final averaging scheme on the lower-order filters generates a class of passband distortion-free linear-phase FIR filters. The new filters are seen to be more robust to changes in transition bandwidth as well as stopband level. Simulation results that compare the present procedure with other well-known methods are also presented