What do we mean by saying that the spectrum of rectangular pulse is
sinc(x) function?
In case you are just wondering what the whole idea is, at all...
A Fourier transform can be just a frequency domain representation of a
time domain function. Time and frequency are... kin and conjugate to
each other.
The spectral width in one domain times the spectral width in the other
domain will be greater than a finite constant (1, usually), which
implies that something narrow in terms of time information will be
wide in terms of frequency information and the converse. The
transform of the rectangle, 2*a*t*sinc(2*PI*f*t), exhibits this
spectral area product in the "f*t" unitless term inside the sinc()
function. Narrowing 't' spreads out the result over broader 'f'.
Jon