HexoDSP/src/dsp/biquad.rs

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// Copyright (c) 2021 Weird Constructor <weirdconstructor@gmail.com>
// This file is a part of HexoDSP. Released under GPL-3.0-or-later.
// See README.md and COPYING for details.
//
// The implementation of this Biquad Filter has been adapted from
// SamiPerttu, Copyright (c) 2020, under the MIT License.
// See also: https://github.com/SamiPerttu/fundsp/blob/master/src/filter.rs
//
// You will find a float type agnostic version in SamiPerttu's code.
// I converted this to pure f32 for no good reason, other than making
// the code more readable (for me).
use std::f32::consts::*;
#[derive(Copy, Clone, Debug, Default)]
pub struct BiquadCoefs {
pub a1: f32,
pub a2: f32,
pub b0: f32,
pub b1: f32,
pub b2: f32,
}
// TODO:
// https://github.com/VCVRack/Befaco/blob/v1/src/ChowDSP.hpp#L339
// more coeffs from there ^^^^^^^^^^^^^ ?
impl BiquadCoefs {
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#[inline]
pub fn new(b0: f32, b1: f32, b2: f32, a1: f32, a2: f32) -> Self {
Self { b0, b1, b2, a1, a2 }
}
/// Returns settings for a Butterworth lowpass filter.
/// Cutoff is the -3 dB point of the filter in Hz.
#[inline]
pub fn butter_lowpass(sample_rate: f32, cutoff: f32) -> BiquadCoefs {
let f = (cutoff * PI / sample_rate).tan();
let a0r = 1.0 / (1.0 + SQRT_2 * f + f * f);
let a1 = (2.0 * f * f - 2.0) * a0r;
let a2 = (1.0 - SQRT_2 * f + f * f) * a0r;
let b0 = f * f * a0r;
let b1 = 2.0 * b0;
let b2 = b0;
BiquadCoefs { a1, a2, b0, b1, b2 }
}
/// Returns the Q for cascading a butterworth filter:
fn calc_cascaded_butter_q(order: usize, casc_idx: usize) -> f32 {
let order = order as f32;
let casc_idx = casc_idx as f32;
let b =
-2.0 * ((2.0 * casc_idx + order - 1.0) * PI / (2.0 * order))
.cos();
1.0 / b
}
/// Returns settings for a lowpass filter with a specific q
#[inline]
pub fn lowpass(sample_rate: f32, q: f32, cutoff: f32) -> BiquadCoefs {
let f = (cutoff * PI / sample_rate).tan();
let a0r = 1.0 / (1.0 + f / q + f * f);
/*
float norm = 1.f / (1.f + K / Q + K * K);
this->b[0] = K * K * norm;
this->b[1] = 2.f * this->b[0];
this->b[2] = this->b[0];
this->a[1] = 2.f * (K * K - 1.f) * norm;
this->a[2] = (1.f - K / Q + K * K) * norm;
*/
let b0 = f * f * a0r;
let b1 = 2.0 * b0;
let b2 = b0;
let a1 = 2.0 * (f * f - 1.0) * a0r;
let a2 = (1.0 - f / q + f * f) * a0r;
BiquadCoefs { a1, a2, b0, b1, b2 }
}
/// Returns settings for a constant-gain bandpass resonator.
/// The center frequency is given in Hz.
/// Bandwidth is the difference in Hz between -3 dB points of the filter response.
/// The overall gain of the filter is independent of bandwidth.
pub fn resonator(sample_rate: f32, center: f32, bandwidth: f32) -> BiquadCoefs {
let r = (-PI * bandwidth / sample_rate).exp();
let a1 = -2.0 * r * (TAU * center / sample_rate).cos();
let a2 = r * r;
let b0 = (1.0 - r * r).sqrt() * 0.5;
let b1 = 0.0;
let b2 = -b0;
BiquadCoefs { a1, a2, b0, b1, b2 }
}
// /// Frequency response at frequency `omega` expressed as fraction of sampling rate.
// pub fn response(&self, omega: f64) -> Complex64 {
// let z1 = Complex64::from_polar(1.0, -TAU * omega);
// let z2 = Complex64::from_polar(1.0, -2.0 * TAU * omega);
// (re(self.b0) + re(self.b1) * z1 + re(self.b2) * z2)
// / (re(1.0) + re(self.a1) * z1 + re(self.a2) * z2)
// }
}
/// 2nd order IIR filter implemented in normalized Direct Form I.
#[derive(Debug, Copy, Clone, Default)]
pub struct Biquad {
coefs: BiquadCoefs,
x1: f32,
x2: f32,
y1: f32,
y2: f32,
}
impl Biquad {
pub fn new() -> Self {
Default::default()
}
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#[inline]
pub fn new_with(b0: f32, b1: f32, b2: f32, a1: f32, a2: f32) -> Self {
let mut s = Self::new();
s.set_coefs(BiquadCoefs::new(b0, b1, b2, a1, a2));
s
}
#[inline]
pub fn coefs(&self) -> &BiquadCoefs {
&self.coefs
}
#[inline]
pub fn set_coefs(&mut self, coefs: BiquadCoefs) {
self.coefs = coefs;
}
pub fn reset(&mut self) {
self.x1 = 0.0;
self.x2 = 0.0;
self.y1 = 0.0;
self.y2 = 0.0;
}
#[inline]
pub fn tick(&mut self, input: f32) -> f32 {
let x0 = input;
let y0 =
self.coefs.b0 * x0
+ self.coefs.b1 * self.x1
+ self.coefs.b2 * self.x2
- self.coefs.a1 * self.y1
- self.coefs.a2 * self.y2;
self.x2 = self.x1;
self.x1 = x0;
self.y2 = self.y1;
self.y1 = y0;
y0
// Transposed Direct Form II would be:
// y0 = b0 * x0 + s1
// s1 = s2 + b1 * x0 - a1 * y0
// s2 = b2 * x0 - a2 * y0
}
}
#[derive(Copy, Clone)]
pub struct ButterLowpass {
biquad: Biquad,
sample_rate: f32,
cutoff: f32,
}
impl ButterLowpass {
pub fn new(sample_rate: f32, cutoff: f32) -> Self {
let mut this = ButterLowpass {
biquad: Biquad::new(),
sample_rate,
cutoff: 0.0,
};
this.set_cutoff(cutoff);
this
}
pub fn set_cutoff(&mut self, cutoff: f32) {
self.biquad
.set_coefs(BiquadCoefs::butter_lowpass(self.sample_rate, cutoff));
self.cutoff = cutoff;
}
fn set_sample_rate(&mut self, srate: f32) {
self.sample_rate = srate;
self.reset();
self.biquad.reset();
self.set_cutoff(self.cutoff);
}
fn reset(&mut self) {
self.biquad.reset();
self.set_cutoff(self.cutoff);
}
#[inline]
fn tick(&mut self, input: f32) -> f32 {
self.biquad.tick(input)
}
}
// Loosely adapted from https://github.com/VCVRack/Befaco/blob/v1/src/ChowDSP.hpp
// Copyright (c) 2019-2020 Andrew Belt and Befaco contributors
// Under GPLv-3.0-or-later
//
// Which was originally taken from https://github.com/jatinchowdhury18/ChowDSP-VCV/blob/master/src/shared/AAFilter.hpp
// Copyright (c) 2020 jatinchowdhury18
/// Implements oversampling with a ratio of N and a 4 times cascade
/// of Butterworth lowpass filters (~48dB?).
#[derive(Debug, Copy, Clone)]
pub struct Oversampling<const N: usize> {
filters: [Biquad; 4],
buffer: [f32; N],
}
impl<const N: usize> Oversampling<N> {
pub fn new() -> Self {
let mut this = Self {
filters: [Biquad::new(); 4],
buffer: [0.0; N],
};
this.set_sample_rate(44100.0);
this
}
pub fn reset(&mut self) {
self.buffer = [0.0; N];
for filt in &mut self.filters {
filt.reset();
}
}
pub fn set_sample_rate(&mut self, srate: f32) {
let cutoff = 0.98 * (0.5 * srate);
let ovr_srate = (N as f32) * srate;
let filters_len = self.filters.len();
for (i, filt) in self.filters.iter_mut().enumerate() {
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let q = BiquadCoefs::calc_cascaded_butter_q(2 * 4, filters_len - i);
filt.set_coefs(BiquadCoefs::lowpass(ovr_srate, q, cutoff));
}
}
#[inline]
pub fn upsample(&mut self, v: f32) {
self.buffer.fill(0.0);
self.buffer[0] = (N as f32) * v;
for s in &mut self.buffer {
for filt in &mut self.filters {
*s = filt.tick(*s);
}
}
}
#[inline]
pub fn resample_buffer(&mut self) -> &mut [f32; N] { &mut self.buffer }
#[inline]
pub fn downsample(&mut self) -> f32 {
let mut ret = 0.0;
for s in &mut self.buffer {
ret = *s;
for filt in &mut self.filters {
ret = filt.tick(ret);
}
}
ret
}
}