A discrete time all pass system has two of its zeros at 2∠45° and
A discrete time all pass system has two of its zeros at 2∠45° and 0. 5∠0°
Which of the following statements is/are correct?
A. It has more zeros at 0.5∠45° and 2∠0°
B. It is always stable
C. It is only stable it the impulse response is two sided
D. It has two poles at 0.5∠-45° and 2∠0°
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Right Answer is:
SOLUTION
For an all pass filter, the location of poles and zeros are reciprocal conjugate of each other.
\({p_1} = \frac{1}{{{{\left( {{z_1}} \right)}^*}}} = \frac{1}{{{{\left( {2{e^{j45^\circ }}} \right)}^*}}}\)
\( = \frac{{0.5}}{{{e^{ - j45^\circ }}}} = 0.5\;{e^{j45^\circ }} = 0.5\angle 45^\circ \)
\({p_2} = \frac{1}{{\left( {{z_2}} \right)}} = \frac{1}{{{{\left( {0.5\;{e^{j0}}} \right)}^*}}} = 2\angle 0^\circ \)
For stability,
∴ The impulse response should be two sided for stability
