GATE EE 2016 Set 1 | Continuous Time Signal Fourier Transform Question 3 | Signals and Systems

GATE EE 2016 Set 1

MCQ (Single Correct Answer)

-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 9 English

GATE EE 2016 Set 1 Signals and Systems - Continuous Time Signal Fourier Transform Question 9 English

Which one of the following statements is TRUE?

x₁(t) and x₂(t) are complex and x₁(t)x₂(t) is also complex with nonzero imaginary part

x₁(t) and x₂(t) are real and x₁(t)x₂(t) is also real

x₁(t) and x₂(t) are complex but x₁(t)x₂(t) is real

x₁(t) and x₂(t) are imaginary but x₁(t)x₂(t) is real

GATE EE 2015 Set 2

MCQ (Single Correct Answer)

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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

$$\frac{2\sin\left(\omega-10\right)}{\omega-10}$$

$$2e^{j10}\frac{\sin\left(\omega-10\right)}{\omega-10}$$

$$\frac{2\sin\left(\omega\right)}{\omega-10}$$

$$e^{j10\omega\frac{2\sin\omega}\omega}$$

GATE EE 2014 Set 3

MCQ (Single Correct Answer)

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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?

X($$\omega$$) and Y($$\omega$$) are both real.

X($$\omega$$) is real and Y($$\omega$$) is imaginary.

X($$\omega$$) and Y($$\omega$$) are both imaginary.

X($$\omega$$) is imaginary and Y($$\omega$$) is real.

GATE EE 2014 Set 2

MCQ (Single Correct Answer)

-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 highly attenuated square wave at 10 kHz

nearly zero.

a nearly perfect cosine wave at 30 kHz.

a nearly perfect sine wave at 30 kHz.