close all
clear all 
clc

load('homework2.mat') % defines t, x, g, T
N = length(x);
X = fftshift(T*fft(x));
G = fftshift(T*fft(g));
om = (-round((N-1)/2):round(N/2)-1) *2*pi/(N*T);          
Y = X.*G;
y = ifft(ifftshift(Y)/T);
y2 = T*conv(x,g);
y2 = y2(1:length(x));

figure(1)
subplot(2,2,1)
plot(t,x)
grid
xlabel('t')
ylabel('x(t)')
title('pancreatic secretion')
subplot(2,2,2)
plot(t,g)
grid
xlabel('t')
ylabel('g(t)')
title('impulse response')
subplot(2,1,2)
plot(t,y,t,y2)
grid
xlabel('t')
ylabel('y(t)')
legend('via fft','via conv')
title('plasma concentration')
sgtitle('time domain')

% printing figure in png format
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 4.5])
print -dpng homework2a.png -r100

figure(2)
subplot(2,2,1)
semilogy(om,abs(X))
grid
xlabel('\omega')
ylabel('X(\omega)')
title('pancreatic secretion')
subplot(2,2,2)
semilogy(om,abs(G))
grid
xlabel('\omega')
ylabel('G(\omega)')
title('transfer function')
subplot(2,1,2)
semilogy(om,abs(Y))
grid
xlabel('\omega')
ylabel('Y(\omega)')
title('plasma concentration')
sgtitle('Fourier domain')

% printing figure in png format
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 6 4.5])
print -dpng homework2b.png -r100