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 ________

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 _____.

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

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.

The signal x(t) is described by

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

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($\omega$)

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

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

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