1
GATE EE 2016 Set 1
+2
-0.6
Suppose x1(t) and x2(t) have the Fourier transforms as shown below. Which one of the following statements is TRUE?
A
x1(t) and x2(t) are complex and x1(t)x2(t) is also complex with nonzero imaginary part
B
x1(t) and x2(t) are real and x1(t)x2(t) is also real
C
x1(t) and x2(t) are complex but x1(t)x2(t) is real
D
x1(t) and x2(t) are imaginary but x1(t)x2(t) is real
2
GATE EE 2015 Set 2
+2
-0.6
Consider a signal defined by $$x\left(t\right)=\left\{\begin{array}{l}e^{j10t}\;\;\;for\;\left|t\right|\leq1\\0\;\;\;\;\;\;\;for\;\;\left|t\right|>1\end{array}\right.$$\$ Its Fourier Transform is
A
$$\frac{2\sin\left(\omega-10\right)}{\omega-10}$$
B
$$2e^{j10}\frac{\sin\left(\omega-10\right)}{\omega-10}$$
C
$$\frac{2\sin\left(\omega\right)}{\omega-10}$$
D
$$e^{j10\omega\frac{2\sin\omega}\omega}$$
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 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.
EXAM MAP
Medical
NEET