# Questions & Answers of Continuous-time and discrete-time Fourier Transform

## Weightage of Continuous-time and discrete-time Fourier Transform

Total 9 Questions have been asked from Continuous-time and discrete-time Fourier Transform topic of Signals and Systems subject in previous GATE papers. Average marks 1.78.

The energy of the signal is ________

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Consider the function $g\left(t\right)={e}^{-t}\mathrm{sin}\left(2\pi t\right)u\left(t\right)$ where $u\left(t\right)$ is the unit step function. The area under $g\left(t\right)$ is _____.

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The Fourier transform of a signal h(t) is $H\left(j\omega \right)=\left(2\mathrm{cos}\omega \right)\left(\mathrm{sin}2\omega \right)/\omega .$The value of h(0) is

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Consider a system whose input x and output y are related by the equation

$\style{font-size:18px}{y\left(t\right)=\int\limits_{-\infty}^\infty x\left(t-\tau\right)h\left(2\tau\right)\operatorname{d}\tau}$

Where h(t) is shown in the graph

Which of the following four properties are possessed by the system?
BIBO: Bounded input gives a bounded output.
Causal: The system is causal.
LP: The system is low pass.
LTI: The system is linear and time invariant.

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The signal x(t) is described by

Two of the angular frequencies at which its Fourier transform becomes zero are

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The impulse response h(t) of a linear time invariant continuous time system is given by

h(t) = exp (-2t)u(t) , where u(t) denotes the unit step function.

The frequency response H($\omega$) of this system in terms of angular frequency $\omega$ is given by H($\omega$)

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The impulse response h(t) of a linear time invariant continuous time system is given by

h(t) = exp (-2t)u(t) , where u(t) denotes the unit step function.

The output of this system to the sinusoidal input x (t) = 2cos (2t) for all time t, is

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The 3-dB bandwidth of the low-pass signal e-tu(t), where u(t) is the unit step function, is given by

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A 5-point sequence x[n] is given as

x[-3] = 1, x[-2] = 1, x[-1] = 0, x[0] = 5, x[1] = 1.

Let $X\left({e}^{j\omega }\right)$ denote the discrete-time Fourier transform of x[n]. The value of $\int\limits_{-\pi}^\pi X\left(e^{j\omega}\right)d\omega$ is