# Fourier Transform of Impulse Train

Why is the fourier transform of impulse train a impulse train? Is there a intuitive reason behind it?

• Another related example of this is the derivative of a square wave. Namely the Fourier transform/series of a square wave is an infinite series of impulses in the frequency domain, whose amplitude is proportional to the inverse of the frequency. Taking the derivative is the same as multiplying by $s$ in the frequency domain, so therefore the amplitudes of the impulses will stay constant. In the time domain the derivative of the square wave looks like periodically and equally spaced positive and negative impulses. – fibonatic Sep 8 '16 at 17:57