The Design of Finite Impulse Response Digital Filters Using Linear Programming Techniques

Many techniques exist for designing digital filters using optimization procedures. Herrmann and Schuessler have designed equiripple error approximations to finite impulse response (FIR) lowpass and bandpass filters using nonlinear programming procedures. 1,2 This work has been extended by Hofstetter, Oppenheim, and Siegel,3 and by Parks and McClellan 4 to solve for the desired filters using polynomial interpolation techniques. Rabiner, Gold, and McGonegal 5 used a steepest descent technique to obtain F I R digital filters with minimax error in selected bands with the constraint that only a few of the filter coefficients were variable. Steiglitz, 0 and Athanasopoulos and Kaiser 7 have used nonlinear optimization techniques to obtain recursive filter approximations to arbitrary frequency response specifications. Recently, attention has been focused 011 the use of linear programming techniques for the design of digital filters. 8-10 Many digital filter design problems are inherently linear in the design parameters, and hence are natural candidates for linear programming optimization. Further, linear programs are easy to implement and are generally guaranteed 1177