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# GATE EC 2022: Signals & Systems Quiz 2 (App update required to attempt this test)

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Question 1

Let and . The value of where

‘*’ represents convolution

‘*’ represents convolution

Question 2

Consider the signal x(t) = te

^{-t}t ≥ 0 otherwise zero. Let X(w) be the Fourier transform of x(t) then findQuestion 3

The complex exponential Fourier series representation of a signal f(t) over the interval (0,T) is

Find the sum of component of f(t) at n = 3 and n = -3

Question 4

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).

Question 5

The power of the signal x(t) up to second harmonics is______.

Question 6

The Fourier transform of is then Fourier transform of is

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May 14ESE & GATE EC

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