Question

x(t) is a positive rectangular pulse from $t=-1tot=+1$ with unit height as shown in the figure. The value of ${\int }_{-\infty }^{\infty }|X\left(\omega \right){|}^{2}d\omega$ where $X\left(\omega \right)$ is the fourier transform of x(t) is

• A. $2\pi$
• B. 2
• C. $4\pi$
• D. 4

Answer 1

The correct option is C $4\pi$

By using Parseval's theorem,
${\int }_{-\infty }^{\infty }|X\left(\omega \right){|}^{2}d\omega =2\pi {\int }_{-1}^{1}1dt=2\pi \times 2$

${\int }_{-\infty }^{\infty }|X\left(\omega \right){|}^{2}d\omega =4\pi$