Question

Find the fourier transform of F(x) = 1, |x|<a0, otherwise.

(a) \(2sin \frac{(ap)}{p} \)

(b) \(2asin \frac{(ap)}{p} \)

(c) \(4sin \frac{(ap)}{p} \)

(d) \(4asin \frac{(ap)}{p} \)

The question was asked by my college professor while I was bunking the class.

I would like to ask this question from Fourier Transform and Convolution in chapter Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Correct choice is (a) \(2sin \frac{(ap)}{p} \)

To elaborate: \(f(p) = \int_{-a}^a e^{ipx} dx \)

\( = \frac{e^{ipx}}{ip} \) from -a to a

\( = \frac{e^{iap}-e^{-iap}}{ip} \)

\( = 2sin \frac{(ap)}{p} \).