Re: [music-dsp] a family of simple polynomial windows and waveforms

OK, I didn't know how you were defining mirror(). On Tue, Aug 9, 2016 at 6:09 AM, Tito Latini wrote: > On Mon, Aug 08, 2016 at 07:05:17PM -0700, James McCartney wrote: > > On Tue, Jul 5, 2016 at 2:42 PM, James McCartney > wrote: > > > > > In the same

Re: [music-dsp] a family of simple polynomial windows and waveforms

On Mon, Aug 08, 2016 at 07:05:17PM -0700, James McCartney wrote: > On Tue, Jul 5, 2016 at 2:42 PM, James McCartney wrote: > > > In the same vein: a family of smoothed sawtooth waves > > > > f(x) = x - x^a > > > > changing this to : > > f(x) = x - sgn(x)*abs(x)^a > > allows

Re: [music-dsp] a family of simple polynomial windows and waveforms

2016-08-09 10:14 GMT+02:00 James McCartney : > > > The original formula created a smoothed sawtooth wave only when 'a' was an > odd integer. > The new formula creates a smoothed sawtooth wave for any real 'a' greater > than 1.0. > > Please apologize my misunderstanding. It is

Re: [music-dsp] a family of simple polynomial windows and waveforms

On Mon, Aug 8, 2016 at 11:56 PM, Uli Brueggemann wrote: > > 2016-08-09 8:49 GMT+02:00 James McCartney : > >> >> >> On Aug 8, 2016, at 23:43, Uli Brueggemann >> wrote: >> >> 2016-08-09 4:05 GMT+02:00 James McCartney

Re: [music-dsp] a family of simple polynomial windows and waveforms

2016-08-09 8:49 GMT+02:00 James McCartney : > > > On Aug 8, 2016, at 23:43, Uli Brueggemann > wrote: > > 2016-08-09 4:05 GMT+02:00 James McCartney : > >> >> >> On Tue, Jul 5, 2016 at 2:42 PM, James McCartney wrote:

Re: [music-dsp] a family of simple polynomial windows and waveforms

2016-08-09 4:05 GMT+02:00 James McCartney : > > > On Tue, Jul 5, 2016 at 2:42 PM, James McCartney wrote: > >> In the same vein: a family of smoothed sawtooth waves >> >> f(x) = x - x^a >> > > changing this to : > > f(x) = x - sgn(x)*abs(x)^a > > allows 'a' to

Re: [music-dsp] a family of simple polynomial windows and waveforms

On Tue, Jul 5, 2016 at 2:42 PM, James McCartney wrote: > In the same vein: a family of smoothed sawtooth waves > > f(x) = x - x^a > changing this to : f(x) = x - sgn(x)*abs(x)^a allows 'a' to be continuously variable, not just an odd integer. sgn(x) is the signum function.

Re: [music-dsp] a family of simple polynomial windows and waveforms

On Tue, Jul 05, 2016 at 02:42:59PM -0700, James McCartney wrote: > In the same vein: a family of smoothed sawtooth waves > > f(x) = x - x^a > > evaluated from x = -1 to +1 > > where 'a' is an odd integer >= 3. > > the greater 'a', the greater number of harmonics. > > plot: > >

Re: [music-dsp] a family of simple polynomial windows and waveforms

Original Message Subject: Re: [music-dsp] a family of simple polynomial windows and waveforms From: "robert bristow-johnson" Date: Sat, June 11, 2016 12:52 am To: music-dsp@music.columbia.edu

Re: [music-dsp] a family of simple polynomial windows and waveforms - DINisnoise

On Tue, Jun 14, 2016 at 5:41 PM, Alan Wolfe wrote: > speaking of Bezier, the graphs shown earlier look a lot like gain ( > http://blog.demofox.org/2012/09/24/bias-and-gain-are-your-friend/) > lots of unipolar warping curves: http://easings.net > and also SmoothStep

Re: [music-dsp] a family of simple polynomial windows and waveforms - DINisnoise

speaking of Bezier, the graphs shown earlier look a lot like gain ( http://blog.demofox.org/2012/09/24/bias-and-gain-are-your-friend/) and also SmoothStep which is y=3x^2+2x^3 Interestingly (to me anyways, before i learned more math) smoothstep is equivelant to a cubic bezier curve where the

Re: [music-dsp] a family of simple polynomial windows and waveforms - DINisnoise

> On Jun 12, 2016, at 3:04 AM, Andy Farnell wrote: > > I did some experiments with Bezier after being hugely inspired by > the sounds Jagannathan Sampath got with his DIN synth. > (http://dinisnoise.org/) DIN is not just an additive synth? appears to be so looking at

Re: [music-dsp] a family of simple polynomial windows and waveforms

On 13/06/2016 3:01 PM, robert bristow-johnson wrote: many hours of integration by parts there's gotta be easier ways of doing it (like Euler's with binomial). I made a Python script for James' polynomial (binomial, Eulers) (sample output is at the bottom of the script). It did take a few

Re: [music-dsp] a family of simple polynomial windows and waveforms

Original Message Subject: Re: [music-dsp] a family of simple polynomial windows and waveforms From: "Ross Bencina" Date: Mon, June 13, 2016 12:25 am To: music-dsp@music.columbia.edu

Re: [music-dsp] a family of simple polynomial windows and waveforms

On 12/06/2016 8:04 PM, Andy Farnell wrote: Great to follow this Ross, even with my weak powers of math its informative. My powers of math are still pretty weak, but I've been spending time at the gym lately ;) I did some experiments with Bezier after being hugely inspired by the sounds

Re: [music-dsp] a family of simple polynomial windows and waveforms

Original Message Subject: Re: [music-dsp] a family of simple polynomial windows and waveforms From: "Ross Bencina" Date: Sat, June 11, 2016 8:24 am To: music-dsp@music.columbia.edu

Re: [music-dsp] a family of simple polynomial windows and waveforms

Hi Andy, On 11/06/2016 9:16 PM, Andy Farnell wrote: Is there something general for the spectrum of all polynomials? I think Robert was referring to the waveshaping spectrum with a sinusoidal input. If the input is a (complex) sinusoid it follows from the index laws: (e^(iw))^2 = e^(i2w)

Re: [music-dsp] a family of simple polynomial windows and waveforms

It is very elegant. Robert, how did you get to that band limit calculation? Is there something general for the spectrum of all polynomials? cheers Andy On Sat, Jun 11, 2016 at 12:52:44AM -0400, robert bristow-johnson wrote: > > > > > > > > Original Message

Re: [music-dsp] a family of simple polynomial windows and waveforms

Original Message Subject: Re: [music-dsp] a family of simple polynomial windows and waveforms From: "Ross Bencina" Date: Sat, June 11, 2016 12:08 am To: music-dsp@music.columbia.edu

Re: [music-dsp] a family of simple polynomial windows and waveforms

Nice! On 11/06/2016 11:31 AM, James McCartney wrote: f(x) = (1-x^a)^b Also potentially interesting for applying waveshaping to quadrature oscillators: https://www.desmos.com/calculator/vlmynkrlbs Ross. ___ dupswapdrop: music-dsp mailing list

[music-dsp] a family of simple polynomial windows and waveforms

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