1
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)
2
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
3
GATE EE 2010
+2
-0.6
x(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown in the figure. The value of $$\int_{-\infty}^\infty\left|X\left(\omega\right)\right|^2d\omega$$ {where X($$\mathrm\omega$$) is the Fourier transform of x(t)} is
A
2
B
2$$\mathrm\pi$$
C
4
D
4$$\mathrm\pi$$
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