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Add part of an FIR crossover

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This includes an algorithm that efficiently converts biquad coefficients
to a linear-phase FIR filter kernel.
This commit is contained in:
Robbert van der Helm 2022-06-06 02:07:26 +02:00
parent 78caa0f78d
commit de13f8c42a
3 changed files with 320 additions and 4 deletions
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1
plugins/crossover/src/crossover.rs
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@ -14,4 +14,5 @@
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <https://www.gnu.org/licenses/>.
pub mod fir;
pub mod iir;

317
plugins/crossover/src/crossover/fir.rs Normal file
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@ -0,0 +1,317 @@
// Crossover: clean crossovers as a multi-out plugin
// Copyright (C) 2022 Robbert van der Helm
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <https://www.gnu.org/licenses/>.
use nih_plug::buffer::ChannelSamples;
use nih_plug::debug::*;
use std::f32;
use std::simd::{f32x2, StdFloat};
use crate::biquad::{Biquad, BiquadCoefficients};
use crate::NUM_BANDS;
// TODO: These filters would be more efficient when processing four samples at a time instead of
// processing two channels at a time. But this keeps the interface nicer.
/// The size of the FIR filter window, or the number of taps.
const FILTER_SIZE: usize = 121;
/// The size of the FIR filter's ring buffer. This is `FILTER_SIZE` rounded up to the next power of
/// two.
const RING_BUFFER_SIZE: usize = FILTER_SIZE.next_power_of_two();
#[derive(Debug)]
pub struct FirCrossover {
/// The kind of crossover to use. `.update_filters()` must be called after changing this.
mode: FirCrossoverType,
/// Filters for each of the bands. Depending on the number of bands argument passed to
/// `.process()` two to five of these may be used. The first one always contains a low-pass
/// filter, the last one always contains a high-pass filter, while the other bands will contain
/// band-pass filters.
band_filters: [FirFilter; NUM_BANDS],
}
/// The type of FIR crossover to use.
#[derive(Debug, Clone, Copy)]
pub enum FirCrossoverType {
/// Emulates the filter slope of [`super::iir::IirCrossoverType`], but with linear-phase FIR
/// filters instead of minimum-phase IIR filters. The exact same filters are used to design the
/// FIR filters.
LinkwitzRiley24LinearPhase,
}
/// A single FIR filter that may be configured in any way. In this plugin this will be a
/// linear-phase low-pass, band-pass, or high-pass filter.
#[derive(Debug, Clone)]
struct FirFilter {
/// The coefficients for this filter. The filters for both channels should be equivalent, this
/// just avoids broadcasts in the filter process.
///
/// TODO: Profile to see if storing this as f32x2 rather than f32s plus splatting makes any
/// difference in performance at all
coefficients: FirCoefficients,
/// A ring buffer storing the last `FILTER_SIZE - 1` samples. The capacity is `FILTER_SIZE`
/// rounded up to the next power of two.
delay_buffer: [f32x2; RING_BUFFER_SIZE],
/// The index in `delay_buffer` to write the next sample to. Wrapping negative indices back to
/// the end, the previous sample can be found at `delay_buffer[delay_buffer_next_idx - 1]`, the
/// one before that at `delay_buffer[delay_buffer_next_idx - 2]`, and so on.
delay_buffer_next_idx: usize,
}
/// Coefficients for an FIR filter. This struct includes ways to design the filter. Parameterized
/// over `f32x2` only for the time being since that's what we need here.
#[repr(transparent)]
#[derive(Debug, Clone)]
struct FirCoefficients([f32x2; FILTER_SIZE]);
impl Default for FirFilter {
fn default() -> Self {
Self {
coefficients: FirCoefficients::default(),
delay_buffer: [f32x2::default(); RING_BUFFER_SIZE],
delay_buffer_next_idx: 0,
}
}
}
impl Default for FirCoefficients {
fn default() -> Self {
// Initialize this to a delay with the same amount of latency as we'd introduce with our
// linear-phase filters
let mut coefficients = [f32x2::default(); FILTER_SIZE];
coefficients[FILTER_SIZE / 2] = f32x2::splat(1.0);
Self(coefficients)
}
}
impl FirCrossover {
/// Create a new multiband crossover processor. All filters will be configured to pass audio
/// through as is, albeit with a delay. `.update()` needs to be called first to set up the
/// filters, and `.reset()` can be called whenever the filter state must be cleared.
///
/// Make sure to add the latency reported by [`latency()`][Self::latency()] to the plugin's
/// reported latency.
pub fn new(mode: FirCrossoverType) -> Self {
Self {
mode,
band_filters: Default::default(),
}
}
/// Get the current latency in samples. This depends on the selected mode.
pub fn latency(&self) -> usize {
// Actually, that's a lie, since we currently only do linear-phase filters with a constant
// size
match self.mode {
FirCrossoverType::LinkwitzRiley24LinearPhase => FILTER_SIZE / 2,
}
}
/// Split the signal into bands using the crossovers previously configured through `.update()`.
/// The split bands will be written to `band_outputs`. `main_io` is not written to, and should
/// be cleared separately.
pub fn process(
&mut self,
num_bands: usize,
main_io: &ChannelSamples,
mut band_outputs: [ChannelSamples; NUM_BANDS],
) {
nih_debug_assert!(num_bands >= 2);
nih_debug_assert!(num_bands <= NUM_BANDS);
// Required for the SIMD, so we'll just do a hard assert or the unchecked conversions will
// be unsound
assert!(main_io.len() == 2);
let mut samples: f32x2 = unsafe { main_io.to_simd_unchecked() };
match self.mode {
FirCrossoverType::LinkwitzRiley24LinearPhase => {
todo!();
}
}
}
/// Update the crossover frequencies for all filters.
pub fn update(
&mut self,
sample_rate: f32,
num_bands: usize,
frequencies: [f32; NUM_BANDS - 1],
) {
match self.mode {
FirCrossoverType::LinkwitzRiley24LinearPhase => todo!(),
}
}
/// Reset the internal filter state for all crossovers.
pub fn reset(&mut self) {
for filter in &mut self.band_filters {
filter.reset();
}
}
}
impl FirFilter {
/// Process left and right audio samples through the filter.
pub fn process(&mut self, samples: f32x2) -> f32x2 {
// TODO: Replace direct convolution with FFT convolution, would make the implementation much
// more complex though because of the multi output part
let coefficients = &self.coefficients.0;
let mut result = coefficients[0] * samples;
// Now multiply `self.coefficients[1..]` with the delay buffer starting at
// `self.delay_buffer_next_idx - 1`, wrapping around to the end when that is reached
// The end index is exclusive, and we already did the multiply+add for the first coefficient.
let before_wraparound_start_idx = self
.delay_buffer_next_idx
.saturating_sub(coefficients.len() - 1);
let before_wraparound_end_idx = self.delay_buffer_next_idx;
let num_before_wraparound = before_wraparound_end_idx - before_wraparound_start_idx;
for (coefficient, delayed_sample) in coefficients[1..1 + num_before_wraparound].iter().zip(
self.delay_buffer[before_wraparound_start_idx..before_wraparound_end_idx]
.iter()
.rev(),
) {
// `result += coefficient * sample`, but with explicit FMA
result = coefficient.mul_add(*delayed_sample, result);
}
let after_wraparound_begin_idx =
self.delay_buffer.len() - (coefficients.len() - num_before_wraparound);
let after_wraparound_end_idx = self.delay_buffer.len();
for (coefficient, delayed_sample) in coefficients[1 + num_before_wraparound..].iter().zip(
self.delay_buffer[after_wraparound_begin_idx..after_wraparound_end_idx]
.iter()
.rev(),
) {
result = coefficient.mul_add(*delayed_sample, result);
}
// And finally write the samples to the delay buffer for the enxt sample
self.delay_buffer[self.delay_buffer_next_idx] = samples;
self.delay_buffer_next_idx = (self.delay_buffer_next_idx + 1) % self.delay_buffer.len();
result
}
/// Update the coefficients for all filters in the crossover.
pub fn update_coefficients(&mut self, coefs: FirCoefficients) {
self.coefficients = coefs;
}
/// Reset the internal filter state.
pub fn reset(&mut self) {
self.delay_buffer.fill(f32x2::default());
self.delay_buffer_next_idx = 0;
}
}
impl FirCoefficients {
/// A somewhat crude but very functional and relatively fast way create a linear phase FIR
/// **low-pass** filter that matches the frequency response of a biquad filter. This normalizes
/// the result, so biquad coefficients for high- and band-pass filters will not work correctly.
/// The algorithm works as follows:
///
/// - An impulse function (so all zeroes except for the first element) of length `FILTER_LEN / 2
/// + 1` is filtered with the biquad.
/// - The biquad's state is reset, and the impulse response is filtered in the opposite
/// direction.
/// - At this point the bidirectionally filtered impulse response contains the **right** half of
/// a truncated linear phase FIR kernel.
///
/// Since the FIR filter will be a symmetrical version of this impulse response, we can optimize
/// the post-processing work slightly by windowing and normalizing this bidirectionally filtered
/// impulse response instead.
///
/// - A half Blackman window is applied to the impulse response. Since this is the right half,
/// this starts at unity gain for the first sample and then tapers off towards the right.
/// - The impulse response is then normalized such that the final linear-phase FIR kernel has a
/// sum of 1.0. Since it will be symmetrical around the IRs first sample, the would-be final
/// sum can be computed as `ir.sum() * 2 - ir[0]`>
///
/// Lastly the linear phase FIR filter simply needs to be constructed from this right half:
///
/// - This bidirectionally filtered impulse response is then reversed, and placed at the start
/// of the `FILTER_LEN` size FIR coefficient array.
/// - The non-reversed bidirectionally filtered impulse response is copied to the second half of
/// the coefficients. (one of the copies doesn't need to include the centermost coefficient)
///
/// The corresponding high-pass filter can be computed through spectral inversion.
pub fn design_linear_phase_low_pass_from_biquad(
biquad_coefs: BiquadCoefficients<f32x2>,
) -> Self {
// We'll start with an impulse...
let mut impulse_response = [f32x2::default(); FILTER_SIZE / 2 + 1];
impulse_response[0] = f32x2::splat(1.0);
// ...and filter that in both directions
let mut biquad = Biquad::default();
biquad.coefficients = biquad_coefs;
for sample in impulse_response.iter_mut() {
*sample = biquad.process(*sample);
}
biquad.reset();
for sample in impulse_response.iter_mut().rev() {
*sample = biquad.process(*sample);
}
// Now `impulse_response` contains a truncated right half of the linear-phase FIR filter. We
// can apply the window function here, and then normalize it so that the the final FIR
// filter kernel sums to 1.
// Adopted from `nih_plug::util::window`
let blackman_scale_1 = (2.0 * f32::consts::PI) / (impulse_response.len() - 1) as f32;
let blackman_scale_2 = blackman_scale_1 * 2.0;
// We only apply the right half of the window, starting at the top of the window
let blackman_offset = impulse_response.len() / 2;
for (sample_idx, sample) in impulse_response.iter_mut().enumerate() {
let i = sample_idx + blackman_offset;
let cos_1 = (blackman_scale_1 * i as f32).cos();
let cos_2 = (blackman_scale_2 * i as f32).cos();
*sample *= f32x2::splat(0.42 - (0.5 * cos_1) + (0.08 * cos_2));
}
// Since this final filter will be symmetrical around
// `impulse_response[0]`, we can simply normalized based on that fact:
let would_be_coefficients_sum =
impulse_response.iter().sum::<f32x2>() * f32x2::splat(2.0) - impulse_response[0];
let would_be_coefficients_recip = would_be_coefficients_sum.recip();
for sample in &mut impulse_response {
*sample *= would_be_coefficients_recip;
}
// And finally we can simply build the filter from the processed impulse response (which,
// again, corresponds to the right half of the final linear-phase filter kernel with the
// first sample in the IR being the middlemost element in the kernel)
let mut coefficients = [f32x2::default(); FILTER_SIZE];
for (coefficient, ir_sample) in coefficients
.iter_mut()
.take(impulse_response.len() / 2 - 1)
// We won't copy the very first sample of the IR here, that will be part of the second
// (non-reversed) half
.zip(impulse_response.iter().skip(1).rev())
{
*coefficient = *ir_sample;
}
// And the second half can be a simple memcpy
coefficients[impulse_response.len() / 2..].copy_from_slice(&impulse_response);
Self(coefficients)
}
}

6
plugins/crossover/src/crossover/iir.rs
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@ -75,7 +75,7 @@ struct AllPassCascade {
impl IirCrossover {
/// Create a new multiband crossover processor. All filters will be configured to pass audio
/// through as it. `.update()` needs to be called first to set up the filters, and `.reset()`
/// through as is. `.update()` needs to be called first to set up the filters, and `.reset()`
/// can be called whenever the filter state must be cleared.
pub fn new(mode: IirCrossoverType) -> Self {
Self {
@ -126,9 +126,7 @@ impl IirCrossover {
}
}
/// Update the crossover frequencies for all filters. If the frequencies are not monotonic then
/// this function will ensure that they are. The active number of bands is used to make sure
/// unused bands are not part of the normalization.
/// Update the crossover frequencies for all filters.
pub fn update(
&mut self,
sample_rate: f32,