I. PREPARATION

%question1
%first define the function
function y=xdis(n)
y=exp(-1*abs(n/10)).*sin((2*pi*n)/4);

clear all
n = -100:100;
xn=xdis(n);
stem(n,xn );
xnSq = xn .* xn;
Ex = sum(xnSq);
disp(['Energy of the signal is: ', num2str(Ex)]);
Px = Ex/length(n);
disp(['Power of the signal is: ', num2str(Px)]);



%question2

n=-150:1:150;
N=25; %Period of the signal
periodicxdis=zeros(1,length(n));
for k=-5:5
    periodicxdis=periodicxdis+xdis(n-k*N);
end


stem(n,periodicxdis)

xn=periodicxdis;
stem(n,xn);
xnSq = xn.^2;
Ex = sum(xnSq);
disp(['Energy of the signal is: ', num2str(Ex)]);
Px = Ex/N;
disp(['Power of the signal is: ', num2str(Px)]);

%question3
t = -10:0.01:10;
gt = 5 * exp(-abs(t/2)) .* cos(2*pi*t);
plot(t, gt);
gtSq = gt.^2;  % Use element-wise power operator instead of multiplication
Ex = trapz(t, gtSq);
Px = Ex/(max(t)-min(t)); 
disp(['The energy of the signal is: ', num2str(Ex)]);
disp(['The power of the signal is: ', num2str(Px)])


%question4
%first define the function
function y=xgt(t)
y=5 * exp(-abs(t/2)) .* cos(2*pi*t);

%in command window periodicxgt


t=-150:150;
N=25;
periodicxgt=zeros(1,length(t));

for k=-5:5
periodicxgt=periodicxgt + xgt(t-k*N);
end

plot(t,periodicxgt)


%in command window 
t=-150:150;

xgtq = periodicxgt.^2;  
Ex = trapz(t, xgtq);
Px = Ex/N; 
disp(['The energy of the signal is: ', num2str(Ex)]);
disp(['The power of the signal is: ', num2str(Px)])