# intuitive interpretation Fourier Transform of two different Rectangular pulses

From my understanding of Fourier transform, a Fourier transform of a signal in time domain will give the different frequency components of the signal in frequency domain, specified by their contributions(energies) in the original.

The Fourier transform of rectangular function is a sinc function

If I take Fourier transform of two different rectangular pulses, with width w1 and w2, with w1>w2, the sinc function of one width w1 is narrow and has large peak as compared to the one with width w2(wider and smaller peak). How do I intuitively understand this behavior?

• Think of the limit cases: a very narrow impulse (ideally a Dirac impulse) contains all frequencies and has a flat spectrum, whereas a constant time domain function has only a DC component, i.e. a Dirac impulse in the frequency domain (at frequency $0$). I.e. the shorter a time domain signal is the wider is its spectrum and vice versa. – Matt L. Sep 10 '14 at 20:40