fun with math: You can create a family of functions, which can be used as windows, LFO waves or envelopes from the formula:
f(x) = (1-x^a)^b evaluated from x = -1 to +1 where 'a' is an even positive integer and 'b' is a positive integer. 'a' controls the flatness of the top and 'b' controls the end tapers. here is a plot: http://i.imgur.com/zoFeMbi.png you can make it into a bipolar wave alternating positive negative like this: x < .5 ? f(4x-1) : -f(4x-3) where x is a unipolar phasor (0 to 1 sawtooth). 4x-1 transforms the interval 0 to .5 into -1 to 1. 4x-3 transforms the interval .5 to 1 into -1 to 1. plot: http://i.imgur.com/8wvnFAE.png -- --- james mccartney
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