Test: Continuous Time Fourier Transformer (CTFT)- 2 - Electronics and Communication Engineering (ECE) MCQ

Fourier transform of x(t) = e^at u (-t), a > 0 is

Determine the fourier transform of the signal x(t) shown in figure.

Match List-I [Function f(t)] with List-II [Fourier transform F(ω)] and select the correct answer using the codes given below the lists:
List- I
A. f(t – t₀)
B. f(t) e^jω0t
C. f₁(t) . f₂(t)


List-ll
1. f(ω – ω₀)
2.
3. 
4.
5.
Codes

Consider a continuous time low pass filter whose impulse response h(t) is known to be real and whouse frequency response magnitude is given by

Determine the value of h(t) if the group delay function is specified as t(ω) = 5.

Consider a signal x₁(t) having a fourier transform x₁(jω). An another signal x₂(t) having fourier transform x₂(jω) is related to x₁ (t) by x₂(jω) = [1 +sgn(ω)] x₁(jω) x₂(t) in terms of x₁(t) is equal to

A Fourier transform pair is as follows:


The Fourier transform of given signal y(t) is

Suppose; y(t) = x(t) cost
and 
then x(t) will be