> > * Since f'(0) != 1 for these curves, they're really more like a > combination gain and soft clipper rather than a pure soft clipper. Does > your approach still work if we impose the constraint that f'(0)=1?
Apologies, I see that you addressed this very thing later in your answer! On Wed, Dec 14, 2016 at 11:47 AM, Ethan Fenn <et...@polyspectral.com> wrote: > Very interesting ideas Robert, thanks. > > Some observations: > > * Regarding the use of a polynomial to limit the range of spurious > frequency components -- a good goal, but if the input signal actually goes > outside [-1,1] this is no longer strictly true. > * Since f'(0) != 1 for these curves, they're really more like a > combination gain and soft clipper rather than a pure soft clipper. Does > your approach still work if we impose the constraint that f'(0)=1? > > 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. > > -Ethan > > > > > On Wed, Dec 14, 2016 at 5:50 AM, Stefan Stenzel < > stefan.sten...@waldorfmusic.de> wrote: > >> Robert, >> >> Thanks, excellent writeup! >> >> Now I wonder, if I drop the condition that it shall be a polynomial and >> replace the term (1-u^2)^N with (0.5+0.5*cos(u*pi))^N, >> wouldn’t this work in a similar way, but with less discontinous >> derivatives at the endpoints 1 and -1? >> >> Stefan >> >> >> > On 12 Dec 2016, at 19:22 , robert bristow-johnson < >> r...@audioimagination.com> wrote: >> > >> > >> > well, it's a different approach to the same problem, but i just added >> my spin at this on Stack Exchange. http://dsp.stackexchange.com/q >> uestions/36202/monotonic-symmetrical-soft-clipping-polynomial (my spin >> is soft clip it.) >> > >> > r b-j >> > >> > >> > >> > ---------------------------- Original Message >> ---------------------------- >> > Subject: Re: [music-dsp] Can anyone figure out this simple, but >> apparently wrong, mixing technique? >> > From: "Bjorn Roche" <bj...@shimmeo.com> >> > Date: Mon, December 12, 2016 8:45 am >> > To: gjberc...@charter.net >> > "A discussion list for music-related DSP" <music-dsp@music.columbia.edu >> > >> > ------------------------------------------------------------ >> -------------- >> > >> > > On Sat, Dec 10, 2016 at 6:35 PM, <gjberc...@charter.net> wrote: >> > > >> > >> >>Message: 1 >> > >> >>Date: Sat, 10 Dec 2016 14:31:37 -0500 >> > >> >>From: "robert bristow-johnson" <r...@audioimagination.com> >> > >> >>To: music-dsp@music.columbia.edu >> > >> >>Subject: [music-dsp] Can anyone figure out this simple, but >> apparently >> > >> >> wrong, mixing technique? >> > >> > >> > >> >>it's this Victor Toth article:?http://www.vttoth. >> > >> com/CMS/index.php/technical-notes/68 and it doesn't seem to make >> sense to >> > >> me. >> > >> >> >> > >> >>it doesn't matter if it's 8-bit offset binary or not, there should >> not >> > >> be a multiplication of two signals in the definition. >> > >> >>i cannot see what i am missing. ?can anyone enlighten me? >> > >> >> > >> Search for "automixer". The author is not mixing individual samples, >> he >> > >> is using observed signal magnitudes (that have time constants >> associated >> > >> with them) to determine desired signal magnitudes, and from those >> > >> desired magnitudes he is calculating channel gains. >> > >> >> > >> At least I hope that's what he's doing. >> > >> >> > >> > i think that the Toth article *is* mixing audio samples. >> > >> > >> > > I've seen people reference this article on StackOverflow. Regardless >> of >> > > intention, it seems like it is causing some confusion. Here's a >> reference >> > > that seems illuminating: >> > > >> > > https://stackoverflow.com/questions/32019246/how-to-mix-pcm- >> audio-sources-java >> > > >> > > -- >> > > Bjorn Roche >> > > @shimmeoapp >> > > _______________________________________________ >> > >> > >> > -- >> > >> > r b-j r...@audioimagination.com >> > >> > "Imagination is more important than knowledge." >> > >> > _______________________________________________ >> > dupswapdrop: music-dsp mailing list >> > music-dsp@music.columbia.edu >> > https://lists.columbia.edu/mailman/listinfo/music-dsp >> >> _______________________________________________ >> dupswapdrop: music-dsp mailing list >> music-dsp@music.columbia.edu >> https://lists.columbia.edu/mailman/listinfo/music-dsp >> > >
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