%-----------------------------------------------------
% Approximation to Fresnel integral 
% From 7.3.32 and 7.3.33 of Abramowitz and Stegum
% Using 7.39 and 7.3.10
% Accurate to 0.002 for 0<x<infinity
% See Parsons p.42 for definition of path loss
%-----------------------------------------------------

x1= [-4:0.1:0];
x2= [0.1:0.1:4];

%--- negative case ---
x1 = -x1;
f_x = (1.0 + 0.926*x1)./(2 + 1.792*x1 + 3.104*x1.^2);
g_x = 1.0             ./(2 + 4.142*x1 + 3.492*x1.^2 + 6.670*x1.^3);

C_z = 0.5 + f_x .* sin(pi/2 * x1.^2) - g_x .* cos(pi/2*x1.^2);
S_z = 0.5 - f_x .* cos(pi/2 * x1.^2) - g_x .* sin(pi/2*x1.^2);
E1 = (1+j)/2 * ((0.5+C_z) - j*(0.5+S_z));

%--- positive case ---
f_x = (1.0 + 0.926*x2)./(2 + 1.792*x2 + 3.104*x2.^2);
g_x = 1.0             ./(2 + 4.142*x2 + 3.492*x2.^2 + 6.670*x2.^3);

C_z = 0.5 + f_x .* sin(pi/2 * x2.^2) - g_x .* cos(pi/2*x2.^2);
S_z = 0.5 - f_x .* cos(pi/2 * x2.^2) - g_x .* sin(pi/2*x2.^2);

E2 = (1+j)/2 * ((0.5-C_z) - j*(0.5-S_z));


plot([-x1 x2], 20*log10(abs([E1 E2])));
grid