# Re: [music-dsp] Time-variant 2nd-order sinusoidal resonator

```
�
i just got in touch with Olli, and this "triangle wave to sine wave" shaper
polynomial is discussed at this Stack Exchange:

https://dsp.stackexchange.com/questions/46629/finding-polynomial-approximations-of-a-sine-wave/46761#46761

---------------------------- Original Message ----------------------------

Subject: Re: [music-dsp] Time-variant 2nd-order sinusoidal resonator

From: "robert bristow-johnson" <r...@audioimagination.com>

Date: Thu, February 21, 2019 1:33 pm

To: "A discussion list for music-related DSP" <music-dsp@music.columbia.edu>

--------------------------------------------------------------------------

>

>

>

>�

> yup. that's a good way to do it, too. i've done this with a 5th-order
> odd-symmetry polynomial (so there were only 3 non-zero coefficients) and had
> harmonics suppressed down 70 dB below the fundamental.

> first generate sawtooth (at your fundamental frequency) with

> limits of -1 and +1 using a simple phase accumulator.

> second, perform abs value (the sawtooth turns into a triangle from 0 to +1).

> third, subtract 1/2 from the triangle, now the limits are from -1/2 to +1/2

> lastly run that into the 5th-order (or higher odd-order, if you like)

> polynomial to get something very close to a sinusoid.

> i thought, years ago, we were discussing this and Olli Niemetalo had
> optimized coefficients for the polynomial.

> r b-j

>

> ---------------------------- Original Message ----------------------------

>

> Subject: Re: [music-dsp] Time-variant 2nd-order sinusoidal resonator

>

>

From: "Phil Burk" <philb...@mobileer.com>

>

> Date: Thu, February 21, 2019 9:25 am

>

> To: "robert bristow-johnson" <r...@audioimagination.com>

>

> "A discussion list for music-related DSP" <music-dsp@music.columbia.edu>

>

> --------------------------------------------------------------------------

>

>> Another approach is to use a Taylor Expansion. It's pretty accurate in the

>> first quadrant. One advantage over the resonator is that it does not drift.

>> Another advantage is that you can do FM without paying the penalty of

>> recalculating the coefficients.

>>

>> Here is some free Java source.

>>

>> https://github.com/philburk/jsyn/blob/master/src/com/jsyn/unitgen/SineOscillator.java

>>

>> Phil Burk

>>

>>

>> On Wed, Feb 20, 2019, 4:12 PM robert bristow-johnson <

>> r...@audioimagination.com> wrote:

>>

>>> personally, i think that phase accumulator and wavetable lookup and

>>> intersample interpolation is the best way to do a time-varying sinusoidal

>>> oscillator,

>

--

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```