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How do I find the LTI system using deconv, when it is connected to more systems and with the final impulse response?

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Yatharth Sood
Yatharth Sood on 20 Dec 2020
Answered: Paul on 20 Dec 2020
I am given a cascade of 3 LTI systems, of which 2 are known, and the first one needs to be found out. I am trying to use deconv(), trying to first convolute the known signals, and then using deconv with that convolution and the final impulse response given, but I am getting 0 as answer. I am very new to MATLAB, and may not be familiar at all with many of its functions.
The question asked.
My code:
n = 0:10;
h2 = heaviside(n) - heaviside(n - 2);
h3 = conv(h2,h2)
d = [1 5 10 11 8 4 1];
h1 = deconv(d,h3)

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Answers (1)

Paul
Paul on 20 Dec 2020
I think heaviside is function from the Symbolic Math Toolbox, but I don't see any symbolic variables defined. In any case, perhaps this is the correct approach:
>> h2=[1 1]; % u[n] - u[n-2]
>> y = [1 5 10 11 8 4 1];
>> [h1,r] = deconv(y,conv(h2,h2))
h1 =
1 3 3 2 1
r =
0 0 0 0 0 0 0
Verify the result
>> conv(h1,conv(h2,h2))
ans =
1 5 10 11 8 4 1

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