Digital filters with equiripple or minimax responses

Abstract

Techniques for determining the coefficients of digital filters which have equiripple or minimax errors are reviewed and occasionally extended. These techniques include: 1) mapping to provide equiripple errors in recursive filters; 2) windows for making Fourier spectrum measurements with minimax leakage; 3) the simplex method of linear programming to provide minimax errors in a nonrecursive filter's time response to a known pulse or Fourier transform of its coefficients; 4) nonlinear programming to provide minimax errors for nominally any response and filter; and 5) an integer programming technique to provide minimax error despite quantizing the coefficients of a nonrecursive filter. Some sources of computer programs embodying these techniques are indicated.