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 vein: a family of smoothed sawtooth waves
>
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 'a' to be continuous
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 clear now.
- Uli
___
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 :
>>
>>>
>>>
>>> On Tue, Jul 5, 2016 at 2:42 PM, James McCartney
>>> 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 :
>
>>
>>
>> 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
> 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:
>>> In the same vein: a family of smoothed sawtooth waves
>>>
>>> f(x) = x - x^a
>>
>> changing this to :
>>
>> f(x) = x - sg
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 be continuously variable, not just an
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.
>
> evaluated from
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:
>
> http://i.imgur.
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:
>
> http://i.imgur.
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:
http://i.imgur.com/dqQQItT.png
On Fri, Jun 10, 2016 at 6:31 PM, James McCartney wrote:
>
> fun with ma
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.co
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 which is y=3x^2+2x^3
>
sho
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 first
> 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 the prominent and low-res FF
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 hou
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.co
many hours of integration by parts
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I encountered a similar family of functions when looking at polynomial
interpolators' analytical spectrum. Every polynomial interpolator can be
re-written as a convolution with a piecewise polynomial function, and the
symmetric piecewise polynomial functions have a convenient basis in the
form (|t
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 Jag
Great to follow this Ross, even with my weak powers of math
its informative.
So, just an application note: of course the idea of "cheap" oscillators
with interesting band limited waveforms, that require no more
than a phasor and arithmetic (multiplies, integer powers, etc) is
a goal.
I did some e
On 12/06/2016 3:05 AM, Andy Farnell wrote:
Does it make any sense to talk about the "spectrum of a polynomial"
over some (periodic) interval (less than infinity)?? Or is that
silly talk?
For the infinite interval:
Expanding the definition of the Fourier transform, for polynomial p:
P(w) = int
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.co
Hi Ross,
Thanks, a great explanation. I had not seen that the function was
to be used as a transfer for shaping a sinusoid, now the
upper bound Robert gave makes sense.
Does it make any sense to talk about the "spectrum of a polynomial"
over some (periodic) interval (less than infinity)?? Or is
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)
I
--- Original Message
>
> Subject: Re: [music-dsp] a family of simple polynomial windows and waveforms
>
> From: "Ross Bencina"
>
> Date: Sat, June 11,
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.co
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.
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musi
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 th
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