1
GATE ECE 2016 Set 2
Numerical
+2
-0
A continuous-time filter with transfer function $$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$ is converted to a discrete time filter with transfer function $$G(Z) = {{2{z^2} - 0.5032\,z} \over {{z^2} - 0.5032z + k}}$$ so that the impulse response of the continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response of the discrete time filter, The value of k is _________________________.
Your input ____
2
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for $$t\, \ge 0$$:
X: Impulse P: 1 $$- {e^{ - t/T}}$$
Y: Unit step Q: t $$- T(1 - {e^{ - t/T}})$$
Z: Ramp R: $${e^{ - t/T}}$$
A
$$X \to R,\,Y \to Q,\,\,Z \to P$$
B
$$X \to Q,\,Y \to P,\,\,Z \to R$$
C
$$X \to R,\,Y \to P,\,\,Z \to Q$$
D
$$X \to P,\,Y \to R,\,\,Z \to Q$$
3
GATE ECE 2015 Set 1
Numerical
+2
-0
In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in Figure (b). If it is desired that the output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than ___________________________
Your input ____
4
GATE ECE 2007
MCQ (Single Correct Answer)
+2
-0.6
The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by
A
$${1 \over {2\pi }}Hz$$
B
$${1 \over {2\pi }}\sqrt {\sqrt 2 - 1\,} Hz$$
C
$$\infty$$
D
1 Hz
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