1
GATE EE 2011
MCQ (Single Correct Answer)
+1
-0.3
A low–pass filter with a cut-off frequency of 30 Hz is cascaded with a high-pass filter with a cut-off frequency of 20 Hz. The resultant system of filters will function as
A
an all-pass filter
B
an all-stop filter
C
an band stop (band-reject) filter
D
a band–pass filter
2
GATE EE 2011
MCQ (Single Correct Answer)
+2
-0.6
The response h(t) of a linear time invariant system to an impulse $$\delta\left(t\right)$$, under initially relaxed condition is $$h\left(t\right)=e^{-t}\;+\;e^{-2t}$$. The response of this system for a unit step input u(t) is
A
$$u\left(t\right)\;+\;e^{-t}\;+\;e^{-2t}$$
B
$$\left(e^{-t}\;+\;e^{-2t}\right)u\left(t\right)$$
C
$$\left(1.5\;-\;e^{-t}\;-\;0.5e^{-2t}\right)u\left(t\right)$$
D
$$\;e^{-t}\delta\left(t\right)\;+\;e^{-2t}u\left(t\right)$$
3
GATE EE 2011
MCQ (Single Correct Answer)
+1
-0.3
The fourier series expansion $$$f\left(t\right)\;=\;a_0\;+\;\sum_{n=1}^\infty a_n\cos\;n\omega t\;+\;b_n\sin\;n\omega t$$$ of the periodic signal shown below will contain the following nonzero terms GATE EE 2011 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 21 English
A
$$a_0\;and\;b_n\;,\;n=1,\;3,\;5,\;..............\infty$$
B
$$a_0\;and\;a_n\;,\;n=1,\;2,\;3,\;..............\infty$$
C
$$a_0\;,\;a_n\;and\;b_n\;,\;n=1,\;2,\;3,\;..............\infty$$
D
$$a_0\;and\;a_n\;,\;n=1,\;3,\;5,\;..............\infty$$
4
GATE EE 2011
MCQ (Single Correct Answer)
+2
-0.6
Let the Laplace transform of a function f(t) which exists for t > 0 be F1(s) and the Laplace transform of its delayed version f(1 - $$\tau$$) be F2(s). Let F1*(s) be the complex conjugate of F1(s) with the Laplace variable set as $$s=\sigma\;+\;j\omega$$. If G(s) =$$\frac{F_2\left(s\right).F_1^\ast\left(s\right)}{\left|F_1\left(s\right)\right|^2}$$ , then the inverse Laplace transform of G(s) is
A
An ideal impulse $$\delta\left(t\right)$$
B
An ideal delayed impulse $$\delta\left(t-\tau\right)$$
C
An ideal step function u(t)
D
An ideal delayed step function $$u\left(t-\tau\right)$$
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