Matlab Systems and Signals Problem [EE]

1. Feb 21, 2010

gshu

1. The problem statement, all variables and given/known data

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

3. 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

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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);

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

Thanks
Greg