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
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