1
GATE ECE 2010
+1
-0.3
For an N-point FFT algorithm with N = $${2^m}$$ which one of the following statements is TRUE?
A
It is not possible to construct a signal flow graph with both input and output in normal order.
B
The number of butterflies in the $${m^{th}}$$ stage is N/m.
C
In-place computation requires storage of only 2N node data.
D
Computation of a butterfly requires only one complex multiplication.
2
GATE ECE 2010
+1
-0.3
Consider the z-transform
X(z)=5$${z^2} + 4{z^{ - 1}} + 3;0 < \left| z \right| < \infty$$.

The inverse z - transform x$$\,\left[ n \right]$$ is

A
$$5\,\delta [n + 2] + 3\,\delta {\rm{\;}}[n]{\mkern 1mu} + 4\delta [n - 1]$$
B
$$5\,\delta [n - 2] + 3\,\delta [n] + 4\,\delta [n + 1]$$
C
$$5\,u[n + 2] + 3\,u[n]{\mkern 1mu} + 4\,u[n - 1]$$
D
$$5\,u[n - 2] + 3\,u[n]{\mkern 1mu} + 4\,u[n + 1]$$
3
GATE ECE 2010
+2
-0.6
A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$.

Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = $${e^{ - 2t}}$$ u(t) is given by

A
$$({e^t} - {e^{3t}})\,u(t)$$
B
$$({e^{ - t}} - {e^{ - 3t}})\,u(t)$$
C
$$({e^{ - t}} + {e^{ - 3t}})\,u(t)$$
D
$$({e^t} + {e^{3t}})\,u(t)$$
4
GATE ECE 2010
+1
-0.3
Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}\left[ n \right]\, = \delta \left[ {n - 2} \right]$$ are connected in cascade. The overall impulse response of the cascaded system is
A
$$\delta \left[ {n - 1} \right] + \delta \left[ {n - 2} \right]$$
B
$$\delta \left[ {n - 4} \right]$$
C
$$\delta \left[ {n - 3} \right]$$
D
$$\delta \left[ {n - 1} \right]\delta \left[ {n - 2} \right]$$
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