function E=ps12_6242_2004(N)
% function E=ps12_6242_2004(N)
%
% estimates H-Infinity norm of (1-exp(-s))/s-1/(1+0.5s)
% larger N means better quality of estimation

if nargin<1, N=10000; end         % default number of samples
W=4*sqrt(N/3);                   % optimal W
e=8/W;                           % error bound
w=(1:N)*W/N;                     % w-samples
s=j*w;                           % s-samples
G=(1-exp(-s))./s;                % G-hamples
Ghat=1./(1+0.5*s);               % Ghat-samples
E=max(abs(G-Ghat));              % calculated H-Infinity norm
fprintf('\nThe norm is between %f and %f\n',E-e,E+e);
close(gcf)
subplot(2,1,1); plot(w,real(G),w,real(Ghat)); grid
subplot(2,1,2); plot(w,imag(G),w,imag(Ghat)); grid