% bpcheb2.m - bandpass Chebyshev type 2 digital filter design % % [A, B, P] = bpcheb2(fs, fpa, fpb, fsa, fsb, Apass, Astop) % % design parameters: % P = [Wpass, Wstop, Wsa, Wsb, c, epass, estop, Nex, N, f3a, f3b, a]; % A, B are Kx5 matrices of cascaded fourth-order sections function [A, B, P] = bpcheb2(fs, fpa, fpb, fsa, fsb, Apass, Astop) c = sin(2*pi*(fpa + fpb)/fs)/(sin(2*pi*fpa/fs) + sin(2*pi*fpb/fs)); Wpass = abs((c - cos(2*pi*fpb/fs)) / sin(2*pi*fpb/fs)); Wsa = (c - cos(2*pi*fsa/fs)) / sin(2*pi*fsa/fs); Wsb = (c - cos(2*pi*fsb/fs)) / sin(2*pi*fsb/fs); Wstop = min(abs(Wsa), abs(Wsb)); epass = sqrt(10^(Apass/10) - 1); estop = sqrt(10^(Astop/10) - 1); Nex = acosh(estop/epass) / acosh(Wstop/Wpass); N = ceil(Nex); r = rem(N,2); K = (N - r) / 2; a = asinh(estop) / N; W3 = Wstop / cosh(acosh(estop)/N); f3a = (fs/pi) * atan((sqrt(W3^2 - c^2 + 1) - W3)/(c+1)); f3b = (fs/pi) * atan((sqrt(W3^2 - c^2 + 1) + W3)/(c+1)); P = [Wpass,Wstop,Wsa,Wsb,c,epass,estop,Nex,N,f3a,f3b,a]; W0 = sinh(a) / Wstop; % reciprocal of text if r==1, G = 1 / (1 + W0); a1 = -2 * c * W0 / (1 + W0); a2 = -(1 - W0) / (1 + W0); A(1,:) = [1, a1, a2, 0, 0]; B(1,:) = G * [1, 0, -1, 0, 0]; else A(1,:) = [1, 0, 0, 0, 0]; B(1,:) = [1, 0, 0, 0, 0]; end for i=1:K, th = pi * (N - 1 + 2 * i) / (2 * N); Wi = sin(th) / Wstop; % reciprocal of text D = 1 - 2 * W0 * cos(th) + W0^2 + Wi^2; G = (1 + Wi^2) / D; b1 = - 4 * c * Wi^2 / (1 + Wi^2); b2 = 2 * (Wi^2 * (2*c*c+1) - 1) / (1 + Wi^2); a1 = 4 * c * (W0 * cos(th) - W0^2 - Wi^2) / D; a2 = 2 * ((2*c*c + 1)*(W0^2 + Wi^2) - 1) / D; a3 = - 4 * c * (W0 * cos(th) + W0^2 + Wi^2) / D; a4 = (1 + 2 * W0 * cos(th) + W0^2 + Wi^2) / D; A(i+1,:) = [1, a1, a2, a3, a4]; B(i+1,:) = G * [1, b1, b2, b1, 1]; end