1
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to
A
$${{\sin (t)} \over {\pi t}}$$
B
$${{\sin (2t)} \over {\pi t}}$$
C
$${{2\sin (t)} \over {\pi t}}$$
D
$${\left( {{{\sin (t)} \over {\pi t}}} \right)^2}$$
2
GATE ECE 2016 Set 3
Numerical
+2
-0
A continuous-time speech signal $${x_a}(t)$$ is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 20 µs for computing each complex multiplication (including multiplications by 1 and −1) and the time required for addition/ subtraction is negligible, then the maximum value of N is __________.
Your input ____
3
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another signal y$$\left[ n \right]$$, then
A
$$y\left[ n \right] = x\left[ n \right]$$
B
$$y\left[ n \right] = x\left[ { - n} \right]$$
C
$$y\left[ n \right] = - x\left[ n \right]$$
D
$$y\left[ n \right] = - x\left[ { - n} \right]$$
4
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $$x\left[ n \right] = \,{\left( {2.0} \right)^{\left| n \right|}}$$ , $$ - \infty < n < + \infty $$ then the ROC of its z-transform is represented by
A
GATE ECE 2016 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 1
B
GATE ECE 2016 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 2
C
GATE ECE 2016 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 3
D
GATE ECE 2016 Set 3 Signals and Systems - Discrete Time Signal Z Transform Question 2 English Option 4
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