Approximation of almost equiripple low-pass FIR filters

A novel approximation of linear phase almost equiripple low-pass finite impulse response filter is introduced. Its frequency response closely approaches the frequency response of an optimal equiripple low-pass finite impulse response filter. The presented approximation is based on the generating polynomial which it is related to the class of iso-extremal polynomials. The closed form solution for an algebraic evaluation of the impulse response of the filter has been developed on the basis of a generalization of the differential equation suitable for the halfband specifications. No numerical procedures are involved. The practical design procedure based on the developed approximation is presented. An example of the design is included.