Question 4.5: Determine the Fourier Transform of the rectangular pulse, wh...

The Fourier transform pairs are as follows:

p(t)=\frac{1}{2\pi } \int_{-\infty }^{\infty } C(\bar{\omega } ) e^{i\bar{\omega }t}d \bar{\omega }            (4.22a)

in which the harmonic amplitude function is given by,

C(\bar{\omega } )=\int_{-\infty }^{\infty }p(t) e^{-i\bar{\omega }t}dt            (4.22b)

Equation (4.22b) gives,

C(\bar{\omega } )=\int_{-T}^{T}p_{0}e^{-i\bar{\omega }t }dt

or,          =\left|-\frac{p_{0}}{i\bar{\omega } }(e^{-i\bar{\omega } t}-e^{i\bar{\omega }t }) \right|^{T}_{-T}

or,           =\frac{ip_{0}}{\bar{\omega } } ((\cos \bar{\omega }T-i\sin \bar{\omega }T )-(\cos\bar{\omega }T+i\sin \bar{\omega }T ))

or,           C(\bar{\omega })=2p_0\left\lgroup \frac{i\sin \bar{\omega }T}{\bar{\omega }T}\right\rgroup  Real function

It can be plotted as shown in Figure 4.8(b).