GATE EE 2006 | GATE EE Year Wise Previous Years Questions

GATE EE 2006

MCQ (Single Correct Answer)

-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

$$y_1\left[n\right]\leftrightarrow Y_1\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(\frac23\right)^nz^{-n}$$

$$y_2\left[n\right]\leftrightarrow Y_2\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(5^n-n\right)z^{-\left(2n+1\right)}$$

$$y_3\left[n\right]\leftrightarrow Y_3\left(z\right)={\textstyle\sum_{n=-\infty}^\infty}2^{-\left|n\right|}z^{-n}$$

$$y_4\left[n\right]\leftrightarrow Y_4\left(z\right)=2z^{-4}\;+\;3z^{-2}+1$$

GATE EE 2006

MCQ (Single Correct Answer)

-0.6

A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,

also has a pole at $$1/2\angle {30^ \circ }$$

has a constant phase response over the $$z$$-plane: $$\arg |H\left( z \right)| = const$$

is stable only if it is anticausal

has a constant phase response over the unit circle: $$\arg |H\left( {{e^{j\Omega }}} \right)| = const$$

GATE EE 2006

MCQ (Single Correct Answer)

-0.6

A continuous-time system is described by $$y\left( t \right) = {e^{ - |x\left( t \right)|}},$$ where $$y(t)$$ is the output and $$x(t)$$ is the input. $$y(t)$$ is bounded

only when $$x(t)$$ is bounded

only when $$x(t)$$ is non-negative

only for $$t \ge 0$$ if $$x(t)$$ is bounded for $$t \ge 0$$

even when $$x(t)$$ is not bounded

GATE EE 2006

MCQ (Single Correct Answer)

-0.6

$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by the difference equation $$y\left[ n \right] - 0.8y\left[ {n - 1} \right] = x\left[ n \right] + 1.25\,x\left[ {n + 1} \right].$$ Its right-sided impulse response is

causal

unbounded

periodic

non-negative

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