1
GATE EE 2016 Set 1
+2
-0.6
The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x(t) is the input signal. A signal z(t) is called eigen-signal of the system T, when T{z(t)}= yz(t), where $$\gamma$$ is a complex number, in general, and is called an eigen value of T. suppose the impulse response of the system T is real and even. Which of the following statements is TRUE?
A
cos(t) is and eigen-signal but sin(t) is not
B
cos(t) is and sin(t) are both eigen-signal but with different eigen values
C
sin(t) is an eigen-signal but cos(t) is not
D
cos(t) and sin(t) are both eigen-signal with identical eigen values
2
GATE EE 2014 Set 3
+2
-0.6
A continuous-time LTI system with system function H($$\omega$$) has the following pole-zero plot. For this system, which of the alternatives is TRUE?
A
$$\left|H\left(0\right)\right|\;>\;\left|H\left(\omega\right)\right|;\;\left|\omega\right|\;>0$$
B
$$\left|H\left(\omega\right)\right|$$ has multiple maxima,at $$\omega_1\;and\;\omega_2$$
C
$$\left|H\left(0\right)\right|\;<\;\left|H\left(\omega\right)\right|;\;\left|\omega\right|\;>0$$
D
$$\left|H\left(\omega\right)\right|=\;cons\;\tan\;t;\;-\infty\;<\;\omega\;<\;\infty$$
3
GATE EE 2010
+2
-0.6
Given f(t) and g(t)as shown below: The Laplace transform of g(t) is
A
$$\frac1s\left(e^{3s}\;-\;e^{5s}\right)$$
B
$$\frac1s\left(e^{-5s}\;-\;e^{-3s}\right)$$
C
$$\frac{e^{-3s}}s\left(1\;-\;e^{-2s}\right)$$
D
$$\frac1s\left(e^{5s}\;-\;e^{3s}\right)$$
4
GATE EE 2010
+2
-0.6
Given f(t) and g(t)as shown below: g(t) can be expressed as
A
g(t) = f(2t - 3)
B
g(t) = $$f\left(\frac t2-3\right)$$
C
g(t) = $$f\left(2t-\frac32\right)$$
D
g(t) = $$f\left(\frac t2-\frac32\right)$$
EXAM MAP
Medical
NEET