Almost Equiripple Low-Pass FIR Filters

An approximation of the linear phase almost equiripple low-pass finite impulse response filter is introduced. The frequency response of an almost equiripple low-pass finite impulse response filter closely approaches the frequency response of an optimal equiripple low-pass finite impulse response filter in the Chebyshev sense. The presented approximation is based on the generating polynomial. Despite that the generating polynomial has no iso-extremal behavior, it is related to the class of iso-extremal polynomials. The zero phase transfer function of an almost equiripple low-pass finite impulse response filter follows from the generating polynomial. The closed form solution for the direct algebraic computation of the impulse response of the filter has been developed on the basis of generalization of the differential equation suitable for the half-band specifications. No numerical procedures are involved. The practical design procedure based on the developed approximation is presented. For illustration of the design procedure one example of the design is included here.