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

The energy of the signal xt = sin4πt4πt is ________

Consider the function gt=e-tsin2πtut where u(t) is the unit step function. The area under g(t) is _____.

The Fourier transform of a signal h(t) is Hjω=2cosωsin2ω/ω. 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

xt=1for -1t+10otherwise

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(ω) of this system in terms of angular frequency ω is given by H(ω)

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

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 Xejω 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