1
GATE EE 2006
MCQ (Single Correct Answer)
+2
-0.6
A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,
A
also has a pole at $$1/2\angle {30^ \circ }$$
B
has a constant phase response over the $$z$$-plane: $$\arg |H\left( z \right)| = const$$
C
is stable only if it is anticausal
D
has a constant phase response over the unit circle: $$\arg |H\left( {{e^{j\Omega }}} \right)| = const$$
2
GATE EE 2006
MCQ (Single Correct Answer)
+2
-0.6
The discrete-time signal $$$x\left[n\right]\leftrightarrow X\left(z\right)={\textstyle\sum_{n=0}^\infty}\frac{3^n}{2+n}z^{2n}$$$ where $$\leftrightarrow$$ denote a transform-pair relationship, is orthogonal to the signal
A
$$y_1\left[n\right]\leftrightarrow Y_1\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(\frac23\right)^nz^{-n}$$
B
$$y_2\left[n\right]\leftrightarrow Y_2\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(5^n-n\right)z^{-\left(2n+1\right)}$$
C
$$y_3\left[n\right]\leftrightarrow Y_3\left(z\right)={\textstyle\sum_{n=-\infty}^\infty}2^{-\left|n\right|}z^{-n}$$
D
$$y_4\left[n\right]\leftrightarrow Y_4\left(z\right)=2z^{-4}\;+\;3z^{-2}+1$$
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