Filter design and equalization - MIT OpenCourseWare

• h is optimization variableChebychev designminimize max | H(ω) − H des (ω) |ω∈[0,π]• H des : R → C is (given) desired transfer function• convex problem• can add constraints, e.g., |h i | ≤ 1sample (discretize) frequency:minimize max |H(ω k ) − H des (ω k )|k=1,...,m• sample points 0 ≤ ω 1 < · · · < ω m ≤ π are fixed (e.g., ω k = kπ/m)• m ≫ n (common rule-of-thumb: m = 15n)• yields approximation (relaxation) of problem aboveFilter design 6