% Mark Wilson 214136683
% Artem Rozenfeld 214152847
%% Question 1a
clear;
t = 0:0.01:10;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + 2*pi/6);
plot(t,y)
xlabel('time');
ylabel('function output')
grid;
legend('x(t)')
title('Question 1a')

%% Question 1b
clear;
t = 0:0.01:10;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + 0);
plot(t,y)
hold on;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + pi/4);
plot(t,y)
hold on;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + pi/2);
plot(t,y)
hold on;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + 3*pi/4);
plot(t,y)
hold on;
y = 0.1*sind(t)+ 0.2*cos(4*pi*t + pi);
plot(t,y)
hold off;
xlabel('time');
ylabel('function output')
grid;
legend('ø = 0','ø = 45','ø = 90','ø = 135','ø = 180')
title('Question 1b')

%% Question 1c
% Yes, X(t) is a periodic signal.
% It is periodic because the signal repeats
% in a set period with a repeating frequency of 2Hz.
% It might look like the function is rising within the
% given time, because the period is larger than the set t.


%% Question 2a
clear;
t = 0:0.01:10;
y = exp(-0.1*pi*t);
plot(t,y)
hold on;
y = exp(-0.1*pi*t).*cos(2*pi*t);
plot(t,y,':r')
hold off;
ylabel('function output');
xlabel('time');
grid;
legend('e(t)','x2(t)');
title('Question 2a')

%% Question 2b
clear;
t = 0:0.01:10;
y = heaviside((exp(-0.1*pi*(t-2)).*cos(2*pi*(t-2))));
plot(t,y)
ylabel('function output');
xlabel('time');
grid;
legend('x2b(t)');
title('Question 2b')


%% Question 3a
clear;
Z = 1 + -3i + (7i*10/(7i+10));
display(Z)


%% Question 3b
clear;
Z = 1 + -3i + (7i*10/(7i+10));
t = 0:0.01:2;
V = 50*sin(10*pi*t);
plot(t,V)
hold on;
I = (50*sin(10*pi*t - atan(imag(Z)/real(Z)))/abs(Z));
plot(t,I)
hold off
ylabel('function output');
xlabel('time');
grid;
legend('V(t)','I(t)');
title('Question 3b')

%% Question 4
clear;
output=squarewave(10,2,300);
hold on;
output=squarewave(10,2,1);
hold on;
output=maxpower(10,2,1);
hold off;
legend('square wave','fundamental square wave','maxpower')
title('Question 4')
%% squarewave
function output = squarewave(v,f,length);
t = 0:0.001:1;
y = 0;
for n=1:2:length
    output = ((4*v)/pi)*((1/n)*sin(n*2*pi*f*t));
    y = output + y;
end
plot(t,y)
ylabel('function output');
xlabel('time');
grid;
legend('show');

end
%% maxpower
function output = maxpower(v,f,length);
t = 0:0.001:1;
y = 0;
for n=1:2:length
    output = ((4*v)/pi)*((1/n)*sin(n*2*pi*f*t));
    y = output + y;
end
y = y.^2;
plot(t,y)
ylabel('function output');
xlabel('time');
grid;
legend('show');

end


%% Question 5a
clear;
t=-5:.001:5;

y=-3.*sign(t).*exp(2i*pi*t+0.25*t);
subplot(2,1,1);

plot(t,real(y));
title('CT signal real');
xlabel('time');
ylabel('function output');

subplot(2,1,2);

plot(t,imag(y));
title('CT signal imaginary ');
xlabel('time');
ylabel('function output');



%% Question 5b
clear;
t=-5:.001:5;

y=-3.*sign(t).*exp(2i*pi*t+0.25*t);
z=y.*rectangularPulse(t/4);
subplot(2,1,1);
plot(t,real(z));
title('Rectangular Pulse Signal real ');
xlabel('time');
ylabel('function output');

subplot(2,1,2);
plot(t,imag(z));
title('Rectangular Pulse Signal imaginary ');
xlabel('time');
ylabel('function output');



%% Question 6
clear;
t = -2:0.01:2;
if (-2<=t<0)
    y = 0.25*t;
    plot(t,y)
    hold on
end
if (0<=t<0.5)
    y = 1.5;
    plot(t,y)
    hold on
end
if (0.5<=t<=2)
    y = -t +2;
    plot(t,y)
    hold off
end

ylabel('function output');
xlabel('time');
grid;
legend('0.25t','1.5','-t+2')
title('Question 6')
axis([-2,2,-0.5,2]);