Question

Derive the Fourier Transform of a rectangular pulse by
a) Differentiating the pulse to form two delta functions
b) Fourier Transforming the derivative
c) Integrating in the frequency domain by dividing by j2πf

Repeat this procedure for the triangle function using a double derivative.

Hence or otherwise, show that if a function has discontinuities in the nth derivative, the sidelobes will fall off as 1/(f^(n+1)).