1
GATE EE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Suppose x1(t) and x2(t) have the Fourier transforms as shown below. GATE EE 2016 Set 1 Signals and Systems - Continuous Time Signal Fourier Transform Question 8 English 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
MCQ (Single Correct Answer)
+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 3
MCQ (Single Correct Answer)
+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.
4
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+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.
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