---------------------------- Original Message ---------------------------- Subject: Re: [music-dsp] Can anyone figure out this simple, but apparently wrong, mixing technique? From: "James McCartney" <asy...@gmail.com> Date: Wed, December 14, 2016 2:15 pm To: music-dsp@music.columbia.edu -------------------------------------------------------------------------- > On Wed, Dec 14, 2016 at 11:07 AM, James McCartney <asy...@gmail.com> wrote: > >> >> >> On Wed, Dec 14, 2016 at 11:03 AM, James McCartney <asy...@gmail.com> >> wrote: >> >>> >>> >>> On Wed, Dec 14, 2016 at 8:47 AM, Ethan Fenn <et...@polyspectral.com> >>> wrote: >>> >>>> >>>> Another interesting family of curves is given by f(x) = x / >>>> (1+x^N)^(1/N) for even N. The fractional power is kind of annoying, but if >>>> you have a hardware square root then you can compute this for N=2,4,8 >>>> easily enough. >>>> >>> >>> extends to all real N > 0 by using absolute value : >>> >>> f(x) = x / (1+abs(x^N))^(1/N) >>> >> >> whoops, just extends to odd N. My graphing program was fooling me. >> > > This is the correct one: > > f(x) = x / (1+abs(x)^N)^(1/N) > i wouldn't trust the discontinuity of the abs(x) with anything other than even N. i sorta see what it's doing. �it goes to a gain of 1/x when x gets large. �it's a gain of 2^(-1/N) when x=1. �i guess you never hit a discontinuity by splicing to a constant. i think you could have a shape parameter with �f(x) = x / (a + abs(x)^N)^(1/N) -- r b-j � � � � � � � � �r...@audioimagination.com "Imagination is more important than knowledge."
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