Analyse the stability of a system given the impulse response h(n) = (l/2) ^ n * u(n) using (1) Laplace transform and (ii) Z-transform
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To analyze the stability of the system given the impulse response \( h(n) = \left(\frac{1}{2}\right)^n u(n) \), we will use both the Laplace transform and the Z-transform. Show more…
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When the input to an LTI system is x[n] = (1/2)^n u[n] + 2^n u[-n-1], the output is y[n] = 6(1/2)^n u[n] - 6(3/4)^n u[n]. (a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC. (b) Find the impulse response of the system for all values of n. (c) Write the difference equation that characterizes the system. (d) Is the system stable? Is it causal?
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