% lhcheb1.m - lowpass/highpass Chebyshev type 1 filter design % % [A, B, P] = lhcheb1(s, fs, fpass, fstop, Apass, Astop) % % s = 1, -1 = lowpass, highpass % design parameters: % P = [Wpass, Wstop, epass, estop, Nex, N, f3, a]; % A, B are Kx3 matrices of cascaded second-order sections function [A, B, P] = lhcheb1(s, fs, fpass, fstop, Apass, Astop) Wpass = tan(pi * fpass / fs); Wpass = Wpass^s; Wstop = tan(pi * fstop / fs); Wstop = Wstop^s; 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(1/epass) / N; W3 = Wpass * cosh(acosh(1/epass)/N); f3 = (fs/pi) * atan(W3^s); % 3dB frequency P = [Wpass, Wstop, epass, estop, Nex, N, f3, a]; W0 = sinh(a) * Wpass; if r==1, G = W0 / (1 + W0); A(1,:) = [1, s*(2*G-1), 0]; B(1,:) = G * [1, s, 0]; else G = 1 / sqrt(1 + epass^2); A(1,:) = [1, 0, 0]; B(1,:) = G * [1, 0, 0]; end for i=1:K, th = pi * (N - 1 + 2 * i) / (2 * N); Wi = Wpass * sin(th); D = 1 - 2 * W0 * cos(th) + W0^2 + Wi^2; G = (W0^2 + Wi^2) / D; a1 = 2 * (W0^2 + Wi^2 - 1) / D; a2 = (1 + 2 * W0 * cos(th) + W0^2 + Wi^2) / D; A(i+1,:) = [1, s*a1, a2]; B(i+1,:) = G * [1, s*2, 1]; end