1
GATE EE 2014 Set 3
+2
-0.6
A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier Transforms are X($$\omega$$) and Y($$\omega$$). Which of the following statements is TRUE?
A
X($$\omega$$) and Y($$\omega$$) are both real.
B
X($$\omega$$) is real and Y($$\omega$$) is imaginary.
C
X($$\omega$$) and Y($$\omega$$) are both imaginary.
D
X($$\omega$$) is imaginary and Y($$\omega$$) is real.
2
GATE EE 2014 Set 2
+2
-0.6
A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is
A
a highly attenuated square wave at 10 kHz
B
nearly zero.
C
a nearly perfect cosine wave at 30 kHz.
D
a nearly perfect sine wave at 30 kHz.
3
GATE EE 2014 Set 1
+2
-0.6
Let f(t) be a continuous time signal and let F($$\omega$$) be its Fourier Transform defined by $$F\left(\omega\right)=\int_{-\infty}^\infty f\left(t\right)e^{-j\omega t}dt$$. Define g(t) by $$g\left(t\right)=\int_{-\infty}^\infty F\left(u\right)e^{-jut}du$$. What is the relationship between f(t) and g(t)?
A
g(t) would always be proportional to f(t)
B
g(t) would be proportional to f(t) if f(t) is an even function
C
g(t) would be proportional to f(t) only if f(t) is a sinusoidal function
D
g(t) would never be proportional to f(t)
4
GATE EE 2012
+2
-0.6
The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omega$$. The value of h(0) is
A
1/4
B
1/2
C
1
D
2
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
EXAM MAP
Joint Entrance Examination