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Question 9.10: Pole-zero plot and frequency response from a transfer functi......

Pole-zero plot and frequency response from a transfer function 2

Draw the pole-zero plot and graph the frequency response for the system whose transfer function is

H(z)=0.0686(z2−1.087z+0.3132)(z2−1.315z+0.6182).\mathrm{H}(z)={\frac{0.0686}{(z^{2}-1.087z+0.3132)(z^{2}-1.315z+0.6182)}}.

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This transfer function can be factored into

H(z)=0.0686(z−0.5435+j0.1333)(z−0.5435−j0.1333)(z−0.6575+j0.4312)(z−0.6575−j0.4312).\mathrm{H}(z)={\frac{0.0686}{(z-0.5435+j0.1333)(z-0.5435-j0.1333)(z-0.6575+j0.4312)(z-0.6575-j0.4312)}}.

The pole-zero diagram is illustrated in Figure 9.18. The magnitude and phase frequency responses of the system are illustrated in Figure 9.19.

9.18
9.19

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