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## 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

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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