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140 Chapter 4 THE z-TRANSFORM
P4.25 A stable, linear and time-invariant system is given by the following system function
H(z) = 4z2 − 2 √ 2z +1
z 2 − 2 √ 2z +4
1. Determine the difference equation representation for this system.
2. Plot the poles and zeros of H(z), and indicate the ROC.
3. Determine the unit sample response h(n) ofthis system.
4. Is this system causal? If the answer is yes, justify it. If the answer is no, find a causal
unit sample response that satisfies the system function.
P4.26 Determine the zero-input, zero-state, and steady-state responses of the system
y(n) =0.9801y(n − 2) + x(n)+2x(n − 1) + x(n − 2), n≥ 0; y(−2) = 1, y(−1) =0
to the input x(n) =5(−1) n u(n).
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