6. Band-Limited Step

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Generating band-limited square waves by adding sine wave harmonics takes a lot of computation. Examining band-limited square waves reveals a similarity which allows a simpler method of synthesis: the ripply shape at the edges of transitions stays the same regardless of frequency.

The ripples are unaffected by frequency (width)

An ideal square wave has a step at each transition between amplitudes; likewise, a band-limited square wave has a band-limited step at each transition. Since the ripples around the transition quickly fade away in either direction, a band-limited step can be practically generated by synthesizing a low frequency band-limited square wave and cutting off the ends. The result, adjusted to start at 0 and end at 1.0, is a very useful band-limited step:

Band-limited step