Synthio: switch to per-note biquad filtering

[jepler]

Not tested on hardware yet, but gives plausible results for the new manual host computer test "synthio/note/biquad.py"

My main reference has been https://www.w3.org/TR/audio-eq-cookbook/

each note can have just 0 or 1 biquad filters, there's not a filter topology.

the filter property can in theory be dynamically updated but I didn't test it; I think there's not actually a sound mathematical theory of how changing the a/b coefficients dynamically affects things, since the internal y state of the filter doesn't make sense when coefficients change. (w3 audio api notes that changing coefficients at runtime can "create unstable biquad filters")

It's also not currently possible to hook up the biquad filter inputs from blocks/LFOs. This is because of laziness, but also because computing the filter coefficients involves a sin() and cos() call, which are costly. If this design is otherwise adequate, but automation of the biquad filters from LFOs is needed, we can find out whether sin/cos are fast enough (or whether a fixed point sin/cos would be adequate & fast enough).

@gamblor21 @todbot

[jepler]

and I verified the filter coefficients against https://arachnoid.com/BiQuadDesigner/

[jepler]

This "survived" testing by @gamblor21 who used it to make some great percussion sounds by frequency-filtering a noise sample... so I dropped it into review status. There are still some potentially useful biquad filters to add, which should be entered as a feature request issue:

• low & high shelf
• notch
• peak

[todbot]

Hi! Sorry I've not been able to get to this until now. I am having a hard time using this. It seems to be geared to creating static filters that do not change. But filters in synths are usually modulated, a common sound being the low-pass filter sweep bwwwowwww sound. E.g. I would like to do something like the below, but I cannot access the function that goes from frequency & q_factor to biquad coeffs a1,a2,b0,b1,b2:

top_f = 1600
q = 0.5
myfilter = synth.low_pass_filter(frequency=top_f, q_factor=q)
note = synthio.Note(frequency= 440, filter=myfilter)
synth.press(note)
while True:
  myfilter.frequency  = (myfilter.frequency - 10) % f
  time.sleep(0.01)

[todbot]

Two other things:

• it appears one cannot set the filter coeffs after instantiation. e.g. this does not work:

def adjust_filter(afilter,w0,Q):  # f,q
    s,c = math.sin(w0), math.cos(w0)
    alpha = s / (2 * Q)
    a0 = 1 + alpha
    afilter.a1 = -2 * c / a0
    afilter.a2 = 1 - alpha / a0
    afilter.b0 = (1 - c) / 2 / a0
    afilter.b1 = 1 - c / a0 
    afilter.b2 = (1 - c) / 2 / a0

• Doing lpf = synth.low_pass_filter(frequency=1600, q_factor=0.5) fails with "extra keyword arguments given" but lpf = synth.low_pass_fitler(1600,0.5) works

[todbot]

Okay this works as expected*:

# synthio_filter_test.py --
# 5 Jun 2023 - @todbot / Tod Kurt
import time, random, board, analogio, audiopwmio, synthio
knob1 = analogio.AnalogIn(board.GP26)
knob2 = analogio.AnalogIn(board.GP27)
audio = audiopwmio.PWMAudioOut(board.GP10)
synth = synthio.Synthesizer(sample_rate=22050)
audio.play(synth)

note1 = synthio.Note(frequency=110)
synth.press(note1)

while True:
    lpf_f = 10 + knob1.value / 32
    lpf_q = knob2.value / 20000
    note1.filter = synth.low_pass_filter(lpf_f, lpf_q)
    print(lpf_f, lpf_q)
    time.sleep(0.1)

• with the exception there are some very nasty instabilities at high resonance values (Q>2.35) and, oddly, with lower Q = ~1.3 and F = ~130Hz.

But otherwise from my hour or so of testing, I say "ship!" This is a really cool feature that's immediately useful.

[gamblor21]

As discussed tested manually. Code looks good to me. Really useful update! Thanks.

[tannewt]

@jepler Any comments wrt todbot's feedback before I do a final review?

[todbot]

I don't think my comments should hold this up. The code is behaving as intended, as this is a common issue with filters at high resonance/feedback values. I'm sure we can devise band-aids as needed later.

[jepler]

Let's slip it in @tannewt !