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An LTI system is characterized by the system function:$ H(z) = \dfrac {z}{(z-\frac 14)(z+\frac14)(z-\frac12)}$
written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 7.0 years ago

write down possible ROCs for different possible ROCs. Determine causality and stability and impulse response of the system.

Mumbai University > EXTC > Sem 4 > Signals and Systems

Marks : 10

Year : DEC 2014
signals and systems
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written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k

$$H(z) = \dfrac z {(z-\frac14)(z+\frac14)(z-\frac12)}$$

Poles at: $z=1/4, -1/4, ½$

enter image description here

Pole zero plot:

Since exterior part of circle (r=1/2) lies within the unit circle. Hence the given system is causal. Also all the pole of the system lies inside the unit circle, thus having bounded output for every bounded input. …

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