% script that visualizes the effects of
% sampling and windowing
global_decl;
platform('octave'); %put either 'octave' or 'matlab'
a = - 10.0; b = 100;
s0 = a + i * b;
t = [0:0.001:1];
y = exp(s0*t); % complex exponential
subplot(2,2,1);  plot(t,real(y));
eval(mygridon);
title('Exponentially-decayed sinusoid');
xlabel('t [s]'); ylabel('y');
eval(myreplot);
pause;
f = [0:0.1:100];
Y = 1 ./ (i * 2 * pi * f - s0*ones(size(f))); 
   % closed-form  Fourier transform
subplot(2,2,2); plot(f, 20*log10(abs(Y)), '-'); 
title('Frequency response of a damped sinusoid');
xlabel('f [Hz]'); ylabel('|Y| [dB]');
hold on;
Fs = 50;
Ysamp = 1 ./ (1 - exp(s0/Fs) * exp(- i*2*pi*f/Fs)) / Fs; 
   % closed-form Fourier transform of the sampled signal
plot(f,20*log10(abs(Ysamp)),'--'); 
n = [0:6];
y = exp(s0*n/Fs);
Ysampw = y * exp(-i*2*pi/Fs*n'*f) / Fs; 
   % Fourier transform of the windowed signal 
   % obtained by vector-matrix multiply
plot(f,20*log10(abs(Ysampw)),'-.');  hold off;
eval(myreplot);

% print -deps2 'sindf.eps');