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

This looks pretty good to me, and I like the amplitude adjustment g[n] term
:)

Depending on the situation you may want to modulate the frequency of the
oscillator pretty fast, so it can help to use a tan approximation function
and then a division and a few other operations to get your cos (w) and sin
(w) rotation terms from that single approximation. I've called the rotation
terms g0 and g1, and c and s are the output cos and sin quadrature
oscillator values

init:
c = cos(2*pi*startphase)
s = sin(2*pi*startphase)

set frequency:
g0 = cos(2*pi*frequency/samplerate)
g1 = sin(2*pi*frequency/samplerate)

or

g = tan(pi*frequency/samplerate);
gg = 2/(1 + g*g)
g0 = gg-1
g1 = g*gg

tick:
t0 = g0*c - g1*s
t1 = g1*c + g0*s
c = t0
s = t1

On Thu, 21 Feb 2019 at 06:28, robert bristow-johnson <
r...@audioimagination.com> wrote:

> i did that wrong.  i meant to say:
>
>    x[n] = a[n] + j*b[n] = g[n-1]*exp(j*w[n]) * x[n-1]
>
> this is the same as
>
>   a[n] = g[n-1]*cos(w[n])*a[n-1] - g[n-1]*sin(w[n])*b[n-1]
>
>   b[n] = g[n-1]*sin(w[n])*a[n-1] + g[n-1]*cos(w[n])*b[n-1]
>
> and adjust the gain g[n] so that |x[n]|^2 = a[n]^2 + b[n]^2 converges to
> the desired amplitude squared (let's say that we want that to be 1).  you
> can adjust the gain slowly with:
>
>   g[n] = 3/2 - (a[n]^2 + b[n]^2)/2
>
> that will keep the amplitude sqrt(a[n]^2 + b[n]^2) stably at 1 even as
> w[n] varies.
>
> i've done this before (when i wanted a quadrature sinusoid) for doing
> frequency offset shifting (not pitch shifting).  worked pretty good.
>
> --
>
>
> r b-j                         r...@audioimagination.com
>
> "Imagination is more important than knowledge."
>
>
>
> > A very simple oscillator recipe is:
> >
> > a(t+1) = C*a(t) - S*b(t)
> > b(t+1) = S*a(t) + C*b(t)
> >
> > Where C=cos(w), S=sin(w), w being the angular frequency. a and b are your
> > two state variables that are updated every sample clock, either of which
> > you can use as your output.
> >
> > There won't be any phase or amplitude discontinuity when you change C and
> > S. However, it's not stable as is, so you periodically have to make an
> > adjustment to make sure that a^2 + b^2 = 1.
> >
> > -Ethan
> >
> >
> > On Wed, Feb 20, 2019 at 12:26 PM Ian Esten <i...@ianesten.com> wrote:
> >
> >> The problem you are experiencing is caused by the fact that after
> changing
> >> the filter coefficients, the state of the filter produces something
> >> different to the current output. There are several ways to solve the
> >> problem:
> >> - The time varying bilinear transform:
> >> http://www.aes.org/e-lib/browse.cfm?elib=18490
> >> - Every time you modify the filter coefficients, modify the state of the
> >> filter so that it will produce the output you are expecting. Easy to do.
> >>
> >> I will also add that some filter structures are less prone to problems
> >> like this. I used a lattice filter structure to allow audio rate
> modulation
> >> of a biquad without any amplitude problems. I have no idea how it would
> >> work for using the filter as an oscillator.
> >>
> >> Best,
> >> Ian
> >>
> >> On Wed, Feb 20, 2019 at 9:07 AM Dario Sanfilippo <
> >> sanfilippo.da...@gmail.com> wrote:
> >>
> >>> Hello, list.
> >>>
> >>> I'm currently working with digital resonators for sinusoidal
> oscillators
> >>> and I was wondering if you have worked with some design which allows
> for
> >>> frequency variations without discontinuities in phase or amplitude.
> >>>
> >>> Thank you so much for your help.
> >>>
> >>> Dario
>
>
>
>
>
>
>
>
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