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This appears to be another name for Boxcar function. Deltahedron ( talk) 07:19, 29 March 2014 (UTC) reply

Or more precisely a special case of it with a unit height and an interval symmetric around the origin. I have tagged it for a proposed merge. — David Eppstein ( talk) 03:44, 31 March 2014 (UTC) reply

The Fourier transform of a step function involves sinc functions. On the other hand, the Fourier series is for a periodic function. What is the reference here? Deltahedron ( talk) 07:39, 29 March 2014 (UTC) reply

The stated definition of this function doesn't say what the period is!! Michael Hardy ( talk) 14:45, 29 March 2014 (UTC) reply

The definition as stated does not make the function periodic, but the characteristic function of an interval. However it appears from the reference [2] that the definition is intended to have it a periodic function. If so, then it is a variant of Square wave. The Fourier series is that of a function of period 1. Perhaps the definition should depend on ${\displaystyle x{\bmod {1}}}$. Deltahedron ( talk) 17:09, 29 March 2014 (UTC) reply