On the design of optimal equiripple FIR digital filters for data transmission applications

An improved linear programming algorithm is required for the design of finite impulse response (FIR) digital filters. This algorithm avoids the numerical ill-conditioning problems which commonly occur due to the necessity to sample the frequency response on a very dense grid of points for high-order filters. This technique is applied to the design of equiripple FIR Nyquist filters and equiripple FIR transmit and receive matched-filters for data transmission applications. The use of linear programming insures that the designs are optimal in the sense that they achieve the maximum possible stopband attenuation for a given filter order and stopband edge frequency. The design algorithm for the matched filters consists of a two-stage process of linear programming to design a Nyquist filter with a nonnegative frequency response followed by standard spectral factorization techniques to extract the nonlinear-phase transmit and receive filters. The design software consists primarily of commonly available FORTRAN subroutine packages for linear programming and polynomial factorization, and is numerically well behaved and very accurate.>