Question 3.22: Filtering Perspective of the Zero-State Response Use the MAT......

Linear Systems and Signals [1311830]

Filtering Perspective of the Zero-State Response

Use the MATLAB filter command to compute and sketch the zero-state response for the system described by $\left(E^2+0.5 E-1\right) y[n]=\left(2 E^2+6 E\right) x[n]$ and the input $x[n]=4^{-n} u[n] .$

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We solve this problem using the same approach as Ex. 3.19. Although the input is bounded and quickly decays to zero, the system itself is unstable and an unbounded output results.

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Script File

>> n = (0:11); x = @(n) 4.^(-n).*(n>=0);
>> a = [1 0.5 -1]; b = [2 6 0]; y = filter(b,a,x(n));
>> clf; stem(n,y,’k’); xlabel(’n’); ylabel(’y[n]’); axis([-0.5 11.5 -20 25]);

3.22

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