railway RRB JE (CBT I + CBT II) Mock Test 2024 Signals and Systems Fourier Transform Properties of Fourier Transform
If x(t) ↔ X(f) denotes a Fourier transform (FT) pair, \(\Pi \left(\dfrac{t}{T}\right)\) denotes a rectangular pulse of width T and '⋆' denotes the convolution operation, then the FT of the signal \(x(t)=\Pi \left(\dfrac{t}{T}\right) * \Pi \left(\dfrac{t}{T}\right)\) is
1
T2 sinc2 (fT)
2
-j sgn (fT)
3
\(T^2 e^{-(F/T)^2}\)
4
T sinc (2fT)