Nummer Zwei

%problem 1
clc
t=-.1:.001:.1;
i1=2.4*cos(15*pi*t-0.8);
i2=4.2*cos(15*pi*t-1.9);
i3=i1+i2;
plot(t,i1);
hold on
plot(t,i2,'-r');
plot(t,i3,'-g');
xlabel('t');
ylabel('current');
title('Current vs Time');
legend('i1','i2','i3')
hold off

%problem 2
clear all
figure
t=-10:1:10;
x=2*US(t+2.5)+2*UR(t+2)-10*US(t+1)-UR(t)...
 -UR(t-1)+US(t-1)+.5*UR(t-2.5)-.5*UR(t-6.5);

plot(t,x)
xlabel('t');
ylabel('x(t)');
title('Signal Plot');

%problem 3
clear all
figure
T=.000125;
t=0.6:T:1.6;
x=t.*(US(t-0.8)-US(t-1.1));
R=2000;
C=.00001;
y=zeros(size(t));
y(1)=0;
for i=2:1:size(t,2) %length(t)
    y(i)=(T*x(i)+R*C*y(i-1))/(R*C+T);
end
plot(t,x,'-r')
hold on
plot(t,y)
xlabel('t');
ylabel('voltage');
title('Low Pass Filter (derivative approx)');
hold off

%problem 4
clear all
figure
T=.000125;
t=0.6:T:1.6;
x=t.*(US(t-0.8)-US(t-1.1));
R=2000;
C=.00001;
y=zeros(size(t));
y(1)=0;
for i=2:1:length(t)
    y(i)=(x(i)+x(i-1)-(1-(T*R*C)/2)*y(i-1))/(1+(T*R*C)/2);
end
plot(t,x,'-r')
hold on
plot(t,y)
xlabel('t');
ylabel('voltage');
title('Low Pass Filter (integral approx)');
hold off

%problem 5
clear all
figure
R=2000;
C=.00001;
T=.000125;
t=-.1:T:.2;
x_imp = zeros(size(t));
x_imp(t==0) = 1/T;
h_actual=(1/(R*C))*exp(-(t/(R*C))).*US(t);
h_approx=zeros(size(t));
h_approx(1)=0;
for i=2:1:length(t)
    h_approx(i)= (T*x_imp(i)+R*C*h_approx(i-1))/(R*C+T);
end
plot(t,h_approx,'-r')
hold on
plot(t,h_actual)
xlabel('t');
ylabel('magnitude');
title('Impulse Responses');
legend('h approx','h actual')
hold off

%problem 6
clear all
figure
T=0.000125;
t=0:T:10;
x= -3*UR(t-1)+3*US(t-1)+3*US(t-2)+3*US(t-3)+3*UR(t-4);
plot(t,x,'-r');
hold on
y=zeros(size(t));
y(1)=2;
y(2)=2-0.35*T;
for i=3:1:length(t)
    y(i)=(x(i)*(.9*T^2+.2*T)-.2*T*x(i-1)-.3*y(i-2)+y(i-1)*(.6+.4*T))/(.3+.4*T+.8*T^2);
end
plot(t,y);
xlabel('t');
ylabel('magnitude');
title('Diff EQ from Prelim');
hold off

%calculations
%i3=2.4*cos(15*pi*t-0.8)+4.2*cos(15*pi*t-1.9)