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/ > questions/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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