Let x(t) = rect t - 1(where rect (x) = 12for - 1 ≤ x

Home » Signals and Systems » Signals and systems electrical engineering miscellaneous » Question

Let x(t) = rect t - 1 (where rect (x) = 1
2

for - 1 ≤ x ≤ 1 and zero otherwise).
2 2

Then if since (x) = sin (πx) ,
πx

then Fourier Transform of x(t) + x(– t) will be given by

1. sinc ω
  2π
2. 2sinc ω
  2π
3. 2sinc ω cos ω
  2π 2
4. sinc ω sin ω
  2π 2

Correct Option: C

rect(x) =1 for	- 1	≤ x ≤	1	.......(1)
	2		2

Given x(t) = rect		t -	1
			2

Simplifying x(t) with the help of equation (1).
∴ x(t) = 1, 0 ≤ t ≤ 1