Matlab Systems and Signals Problem [EE]

[gshu]

Homework Statement

Questions
We ¯rst model the vocal tract by a simple second-order di®erential equation:
d2y(t)/dt2 + B1dy(t)/dt+ C1y(t) = A1x(t);
where A1 = 3:8469 £ 106, B1 = 325:6907, and C1 = 3:8469 . We denote
this system by H1. Here, t is in seconds.
Step 1.) Use MATLAB to compute and plot the impulse response h1(t) and the
unit step response g1(t) of H1.
Hints: use MATLAB's impulse and step functions.
1
For example, \Ts=1e-004; t=[0.0:Ts:0.1]; num1=[A1]; den1=[1 B1 C1];
sys1=tf(num1, den1); h1=impulse(sys1, t), figure; plot(t, h1)".
Step 2.) Assume the input x1(t) to H1 is given by
x1(t) =
1; when 0 <= t <= 5.0 * 10^-4;
0; otherwise:
(2)
Compute and plot the output y1(t) using MATLAB.
Hints: Create the input x1(t) by Ts=1e-004; x1=ones(5,1)", and then
compute the output by \y1=conv(x1, h1)*Ts

The Attempt at a Solution

I'm 99% sure I got Question 1 with the following MATLAB code:
A1 = 3.8469*10^6;
B1 = 325.6907;
C1 = 3.8469*10^6;

num = [ A1 ];
den = [ 1 B1 C1 ];

tfunct = tf(num, den);
Ts = 1e-004;
t =[0.0:Ts:0.1];
h1 = impulse(tfunct, t), figure;
plot(t, h1);

It works and I get a plot

-----
With question 2 I can't figure out how the hint is supposed to factor in the input x1(t). It somehow uses 'ones(5,1)', then conv( ones(5,1), h1); (where h1 is impulse from question 1).
The answer I get definitely doesn't seem right though. This is my attempt at it:

A1 = 3.8469*10^6;
B1 = 325.6907;
C1 = 3.8469*10^6;

num = [ A1 ];
den = [ 1 B1 C1 ];

tfunct = tf(num, den);

Ts = 1e-004;
x1 = ones(5,1);

t =[0.0:Ts:0.1];
h1 = impulse(tfunct, t);
y1 = (conv(x1, h1)*Ts);
figure;
plot(y1, t);

---------
I'm just really not sure how input with constraints is factored in through the 'ones' function. Any ideas??

Thanks
Greg

 

[KataKoniK]

Hello Greg,

Thank you for sharing your code and for asking for help. It looks like you are on the right track with your solution for question 1. For question 2, the hint is suggesting that you create the input x1(t) using the 'ones' function and then use the 'conv' function to convolve it with the impulse response h1(t). This will give you the output y1(t). Here is a possible solution:

A1 = 3.8469*10^6;
B1 = 325.6907;
C1 = 3.8469*10^6;

num = [ A1 ];
den = [ 1 B1 C1 ];

tfunct = tf(num, den);

Ts = 1e-004;
t =[0.0:Ts:0.1];
h1 = impulse(tfunct, t);

x1 = ones(1, length(t));
x1(t>5e-4) = 0; % set values after 5e-4 to 0

y1 = conv(x1, h1)*Ts;

figure;
plot(t, y1);

I hope this helps. Let me know if you have any further questions.