Question

Matlab help

1) Given the functions x1()= tu()-tuft-1) and X2(t)=10e-5,11(), do the following: 1. Plotx,(t) and x2(0) using MATLAB 2. Use MATLAB to find and plot x(0=x:@*.x2(t), where * denotes convolution. 3. Find x(t)=x;()*X2(1) by hand using Laplace transforms. 4. Plot the result of part 3 in MATLAB and compare it to that found in part 2. 2) Given the transfer function shown below, do the following: 1. Find the system's impulse response and plot it using MATLAB 2. Repeat (1), but use the MATLAB command "mpulse to obtain the impulse response. Are both responses the same? 3. Use MATLAB to find the system's response y() for the following inputs: 4. x(t)-12 u(t) 5. x()-10r u(t) 6. x(t)-100cos(200t) u(. How does the magnitude of the output signal compare to that of the input signal? 7. Use MATLAB to obtain the Bode diagram of the system. What type of filter does this system resemble? You must hand in the answers to parts 1 and 4, the plots required by parts 1 thru 4, and your MATLAB script. H(s) 1,000(s +5) » Y(s) (S)(s +6)(s +5-15(s+5+15i)Y(S)

Answer 1

I-So 45 - loQ Pactsal rackon expan nt 10 to 2 SS5 St a. 스10

S 2

MATLAB:

clc;clear all;close all;
t=0:0.01:5
x1=(t.*(t>=0))-(t.*(t>=1))
x2=10*(exp(-5*t))
y=conv(x1,x2)
m=0:0.01:10
subplot(221)
plot(t,x1,'r','linewidth',3)
xlabel('t');ylabel('x1(t)');title('x1(t)')

subplot(222)
plot(t,x2,'b','linewidth',3)
xlabel('t');ylabel('x2(t)');title('x2(t)')

subplot(223)
plot(m,y/100,'m','linewidth',3)
xlabel('t');ylabel('x(t)');title('x(t)=x1*x2')

%from hand calculation
t=0:0.01:10
y1=((2*t)-0.4 +(0.4*(exp(-5*t)))).*(t>=0)
y2=((2*(t-1))-0.4 +(0.4*(exp(-5*(t-1))))).*(t>=1)
y3=(-2+(2*exp(-5*(t-1)))).*(t>=1)
yy=y1-y2+y3
subplot(224)
plot(t,yy,'g','linewidth',3)
xlabel('t');ylabel('x(t)');title('x(t)=x1*x2')

x1(t) x2(t) 10 0.8 ︵ 0.6 4 0.4 0.2 2 4 3 4 x(t)-x1*x2 x(t)=x1 *x2 2 2 1.5 1.5 0.5 0.5 6 8 10 2 6 8 10 4 4