% trigfield5.m investigates the distribution of F(0)

m    = 20;                                  % number of Fourier modes
Cmax = 10000;                               % number of replications
Z    = [];                                  % clear the value of Z

for C = 1:Cmax,                             % run through iid replications
  A    = randn(1,m)*sqrt(2/m);              % amplitudes A
  phi  = 2 * pi * rand(m,1);                % random phase
  Z(C) = A * cos(phi);                      % field value at (x,y)=(0,0)
end

S = sort(Z);                                % sorted field values
p = norminv(((1:Cmax)-0.5)/Cmax);           % standard normal percentiles

clf                                         % clear the current figure

subplot(2,1,1)
plot(p,S,'*');
axis([-4 4 -4 4]);
title('Normal probability plot');

subplot(2,1,2)
hist(S,30);
axis([-4 4 0 Cmax/8]);
title('Histogram of field values');

fprintf('Z has mean %8.4f and variance %8.4f\n',mean(Z), var(Z))