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. >

[1]  Günter Wackersreuther.  Some new aspects of filters for filter banks , 1986, IEEE Trans. Acoust. Speech Signal Process..

[2]  G. Ungerboeck,et al.  Optimum FIR Transmitter and Receiver Filters for Data Transmission Over Band-Limited Channels , 1982, IEEE Trans. Commun..

[3]  T. Barnwell,et al.  A procedure for designing exact reconstruction filter banks for tree-structured subband coders , 1984, ICASSP.

[4]  O. Herrmann,et al.  Design of nonrecursive digital filters with minimum phase , 1970 .

[5]  Victor B. Lawrence,et al.  Design and implementation of transmitter and receiver filters with periodic coefficient nulls for digital systems , 1982, ICASSP.

[6]  L. Rabiner.  Linear program design of finite impulse response (FIR) digital filters , 1972 .

[7]  R W Lucky,et al.  Principles of data communication , 1968 .

[8]  Gian Antonio Mian,et al.  A fast procedure to design equiripple minimum-phase FIR filters , 1982 .

[9]  F. Mintzer,et al.  On half-band, third-band, and Nth-band FIR filters and their design , 1982 .

[10]  L. Rabiner.  The design of finite impulse response digital filters using linear programming techniques , 1972 .

[11]  K. Mueller.  A new approach to optimum pulse shaping in sampled systems using time-domain filtering , 1973 .

[12]  C. J. Wellekens,et al.  Optimal design of minimum-phase FIR filters , 1983 .

[13]  K. Steiglitz.  Optimal design of FIR digital filters with monotone passband response , 1979 .

[14]  Junn-Kuen Liang,et al.  Design of optimal Nyquist, partial response, Nth band, and nonuniform tap spacing FIR digital filters using linear programming techniques , 1985 .

[15]  T. Saramaki,et al.  A class of FIR Nyquist (Nth-band) filters with zero intersymbol interference , 1987 .

[16]  L. Rabiner,et al.  A computer program for designing optimum FIR linear phase digital filters , 1973 .