%question1

%function a
function y=a(t)
y=10*cos(100*pi*t);

%function b
function y=b(t)
y=40*cos(60*pi*t) + 20*sin(40*pi*t);  


t = -0.1:0.0001:0.1;
figure
plot(t, a(t));  % Plot the signal a
figure
plot(t, b(t));  % Plot the signal b

%question1a

Ta=0.02;
t = -Ta/2:0.0001:Ta/2;

energya = trapz(t, a(t).^2)
powera = energya /Ta

disp(['Energy of the a signal is: ', num2str(energya)])
disp(['Power of the a signal is: ', num2str(powera)])



Tb=0.1;
t = -Tb/2:0.0001:Tb/2;

energyb = trapz(t, b(t).^2)
powerb = energyb /Tb

disp(['Energy of the a signal is: ', num2str(energyb)])
disp(['Power of the a signal is: ', num2str(powerb)])

%question1b

Tb=0.1;  
t = -Tb/2:0.0001:Tb/2;
ab=a(t)+b(t);
plot(t, ab);  % Plot the signal ab

energyab = trapz(t, ab.^2)
powerab = energyab / Tb;

disp(['Energy of the ab signal is: ', num2str(energyab)])
disp(['Power of the ab signal is: ', num2str(powerab)])


%question2

%first define the functions
function y=f1(n)
y=2*((0.9).^n).*sin((2*pi*n)/4);

%first define the function
function y=f2(n)
y=(cos((2*pi*(n+1))/12).*stepDT(n+1)) - (cos((pi*n)/6).*stepDT(n));

%first define the function
function y=f3(n)
y=((3*n+6)/10).*exp(-2*n);

%in command window
n=-100:100;
n3=-1:0.1:10;

subplot(3,1,1)
 stem(n, f1(n),'r')
subplot(3,1,2)
 stem(n, f2(n),'k')
subplot(3,1,3)
 stem(n3, f3(n3),'m')


%in command window
n=-100:100;
n3=-1:0.1:10;

energy1=sum(abs(f1(n)).^2);
power1=energy1/length(n);

disp(['Energy of the 1st signal is : ', num2str(energy1)])
disp(['Power of the 1st signal is : ', num2str(power1)])

energy2=sum(abs(f2(n)).^2);
power2=energy2/length(n);

disp(['Energy of the 2nd signal is : ', num2str(energy2)])
disp(['Power of the 2nd signal is : ', num2str(power2)])

energy3=sum(abs(f3(n3)).^2);
power3=energy3/length(n3);

disp(['Energy of the 3rd signal is : ', num2str(energy3)])
disp(['Power of the 3rd signal is : ', num2str(power3)])