Digital filters with equiripple or minimax responses

TLDR: In this paper, various techniques for determining the coefficients of digital filters which have equiripple or minimax errors are reviewed and occasionally extended, such as mapping, nonlinear programming, and integer programming.

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.