square wave frequency representation
The transform of a single rectangular pulse is a Sinc function.  Each added translation of that pulse adds a twisted repitition of that Sinc.  The twist will equal 2 pi at all spectral distances that are odd integer multiples of the reciprocal of the repeat period.  Repeat, and eventually all the twisted portions will all cancel out (form circles in the complex plane around zero) except at those points representing the odd harmonics.  Thus an infinite repeating square wave will be left with only non-zero spectrum at odd harmonics in its transform.