Maximum entropy method and the design of linear phase FIR filters

A procedure that makes use of the maximum-entropy method (MEM) for the design of linear-phase FIR 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. Further, an iterative algorithm makes the design procedures very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize any residual distortion in the passband region, a final averaging scheme on the lower-order filters generates a class of linear phase FIR filters that are practically distortion free in the passband as well as the stopband. Simulation results that compare the present procedure with other well-known methods are also presented