%question1

%define the tri function 

function y=tri(n)
y=rampDT(n+10)-2*rampDT(n)+rampDT(n-10);

%in the command window
n = -50:50;
y = tri(n);

stem(n, y);
xlabel('n');
ylabel('y');
title('Triangular waveform');


%question2
n=-150:150;
N=25; %Period of the signal
periodicTriangle=zeros(1,length(n));
for k=-5:5
    periodicTriangle=periodicTriangle+tri(n-k*N);
end
figure(1)
stem(n,tri(n),'r')
figure(2)
stem(n,periodicTriangle)


%question3

%define the tricon function 
function y=tricon(t)
y=ramp(t+10)-2*ramp(t)+ramp(t-10);


%in the command window
n = -50:50;
y = tricon(n);

plot(n, y);
xlabel('n');
ylabel('y');
title('Triangular waveform');

%in the command window

n=-150:150;
N=25; %Period of the signal
periodicTriangle=zeros(1,length(n));
for k=-5:5
    periodicTriangle=periodicTriangle+tricon(n-k*N);
end
figure(1)
plot(n,tricon(n),'r')
figure(2)
plot(n,periodicTriangle)


%question4

%define the function 

function y = rect(t)
y = u(t + 5) - u(t - 5);

%define the function 

%in the command window
t = -20:0.01:20;
n = -20:20;

xDT = rectDT(n);
x = rect(t);
figure(1)
plot(t,x);
figure(2)
stem(n,xDT);

%question5

%in the command window

t=-150:150;
T=30; %Period of the signal
periodicRectangleCT=zeros(1,length(t));
for k=-5:5
    periodicRectangleCT=periodicRectangleCT+rect(t-k*T);
end
figure(1)
plot(t,rect(t),'r')
figure(2)
plot(t,periodicRectangleCT)

%in the command window

n=-150:150;
N=30; %Period of the signal
periodicRectangle=zeros(1,length(n));
for k=-5:5
    periodicRectangle=periodicRectangle+rectDT(n-k*N);
end
figure(1)
stem(n,rectDT(n),'r')
figure(2)
stem(n,periodicRectangle)

%question8

%in the command window
t=-9000:0.1:9000;
xt=rect((t-3)/10);
xt_sq=xt.^2;
energy=trapz(t,xt_sq);
disp('Energy of the signal is: ');
disp(energy);

%in the command window
t = -9000:0.1:9000;
xt = rect((t-3)/10);
xt_sq = xt.^2;
energy = trapz(t, xt_sq);
disp(['Energy of the signal is: ', num2str(energy)]);