� 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." � � � �
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