GATE EE 2021 : Signals and Systems Quiz 5 (App update required to attempt this test)

Consider a signal,  The value of

[Where X(ω) is the Fourier Transform of x(t)]

Find the value of, where x(t) is given by

An ideal second order Low pass filter is shown below with cut off frequency of 2 rad/sec is supplied with input, x(t) = e^-2t u(t)

Find the energy present in the response of the system (in joules).

Let the fourier transform of a signal x(t) be X(jω).

Then the value of X(0) is ______.

Let X(ω) denote the fourier transform of the signal x(t) depicted in the figure below. Find X(0) = ?

Evaluate the Fourier transform of