Question

Write a MATLAB function that implements the difference equation for the system assuming null initial conditions. Include source code .

y(n) = x(n) + 2x(n-1) + x(n-2) + 0.8 y(n-1) - 0.64 y(n-2)

Use Matlab to calculate the response of the system to p(n) = 0 for all n expect when p(10) = 1.

Using stem, plot the resulting output to n=100

What is the amplitude of the output squence? Was the signal amplified? How much?

Answer 1

code for output response in below

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%input described in question is a unit inpulse function shifted 10 unit
x=zeros(100,1);
x(10)=1; % delta(n-10)
y=[0 0]; % response
for n=3:100
y=[y,x(n) + 2*x(n-1) + x(n-2) + 0.8*y(n-1) - 0.64*y(n-2)]; %difference equation
end
stem(y,'filled'); % plot output response

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plot

in above plot, we can see that amplitude of the output is above 2.5 which dies out after some time thus it is amplified.