pounder_test/dsp/src/iir.rs

156 lines
5.5 KiB
Rust

use miniconf::MiniconfAtomic;
use serde::Deserialize;
use super::{abs, copysign, macc, max, min};
use core::f32;
/// IIR state and coefficients type.
///
/// To represent the IIR state (input and output memory) during the filter update
/// this contains the three inputs (x0, x1, x2) and the two outputs (y1, y2)
/// concatenated. Lower indices correspond to more recent samples.
/// To represent the IIR coefficients, this contains the feed-forward
/// coefficients (b0, b1, b2) followd by the negated feed-back coefficients
/// (-a1, -a2), all five normalized such that a0 = 1.
pub type Vec5 = [f32; 5];
/// IIR configuration.
///
/// Contains the coeeficients `ba`, the output offset `y_offset`, and the
/// output limits `y_min` and `y_max`.
///
/// This implementation achieves several important properties:
///
/// * Its transfer function is universal in the sense that any biquadratic
/// transfer function can be implemented (high-passes, gain limits, second
/// order integrators with inherent anti-windup, notches etc) without code
/// changes preserving all features.
/// * It inherits a universal implementation of "integrator anti-windup", also
/// and especially in the presence of set-point changes and in the presence
/// of proportional or derivative gain without any back-off that would reduce
/// steady-state output range.
/// * It has universal derivative-kick (undesired, unlimited, and un-physical
/// amplification of set-point changes by the derivative term) avoidance.
/// * An offset at the input of an IIR filter (a.k.a. "set-point") is
/// equivalent to an offset at the output. They are related by the
/// overall (DC feed-forward) gain of the filter.
/// * It stores only previous outputs and inputs. These have direct and
/// invariant interpretation (independent of gains and offsets).
/// Therefore it can trivially implement bump-less transfer.
/// * Cascading multiple IIR filters allows stable and robust
/// implementation of transfer functions beyond bequadratic terms.
///
/// # Miniconf
///
/// `{"y_offset": y_offset, "y_min": y_min, "y_max": y_max, "ba": [b0, b1, b2, a1, a2]}`
///
/// * `y0` is the output offset code
/// * `ym` is the lower saturation limit
/// * `yM` is the upper saturation limit
///
/// IIR filter tap gains (`ba`) are an array `[b0, b1, b2, a1, a2]` such that the
/// new output is computed as `y0 = a1*y1 + a2*y2 + b0*x0 + b1*x1 + b2*x2`.
/// The IIR coefficients can be mapped to other transfer function
/// representations, for example as described in <https://arxiv.org/abs/1508.06319>
#[derive(Copy, Clone, Debug, Default, Deserialize, MiniconfAtomic)]
pub struct IIR {
pub ba: Vec5,
pub y_offset: f32,
pub y_min: f32,
pub y_max: f32,
}
impl IIR {
pub const fn new(gain: f32, y_min: f32, y_max: f32) -> Self {
Self {
ba: [gain, 0., 0., 0., 0.],
y_offset: 0.,
y_min,
y_max,
}
}
/// Configures IIR filter coefficients for proportional-integral behavior
/// with gain limit.
///
/// # Arguments
///
/// * `kp` - Proportional gain. Also defines gain sign.
/// * `ki` - Integral gain at Nyquist. Sign taken from `kp`.
/// * `g` - Gain limit.
pub fn set_pi(&mut self, kp: f32, ki: f32, g: f32) -> Result<(), &str> {
let ki = copysign(ki, kp);
let g = copysign(g, kp);
let (a1, b0, b1) = if abs(ki) < f32::EPSILON {
(0., kp, 0.)
} else {
let c = if abs(g) < f32::EPSILON {
1.
} else {
1. / (1. + ki / g)
};
let a1 = 2. * c - 1.;
let b0 = ki * c + kp;
let b1 = ki * c - a1 * kp;
if abs(b0 + b1) < f32::EPSILON {
return Err("low integrator gain and/or gain limit");
}
(a1, b0, b1)
};
self.ba.copy_from_slice(&[b0, b1, 0., a1, 0.]);
Ok(())
}
/// Compute the overall (DC feed-forward) gain.
pub fn get_k(&self) -> f32 {
self.ba[..3].iter().sum()
}
/// Compute input-referred (`x`) offset from output (`y`) offset.
pub fn get_x_offset(&self) -> Result<f32, &str> {
let k = self.get_k();
if abs(k) < f32::EPSILON {
Err("k is zero")
} else {
Ok(self.y_offset / k)
}
}
/// Convert input (`x`) offset to equivalent output (`y`) offset and apply.
///
/// # Arguments
/// * `xo`: Input (`x`) offset.
pub fn set_x_offset(&mut self, xo: f32) {
self.y_offset = xo * self.get_k();
}
/// Feed a new input value into the filter, update the filter state, and
/// return the new output. Only the state `xy` is modified.
///
/// # Arguments
/// * `xy` - Current filter state.
/// * `x0` - New input.
pub fn update(&self, xy: &mut Vec5, x0: f32, hold: bool) -> f32 {
let n = self.ba.len();
debug_assert!(xy.len() == n);
// `xy` contains x0 x1 y0 y1 y2
// Increment time x1 x2 y1 y2 y3
// Shift x1 x1 x2 y1 y2
// This unrolls better than xy.rotate_right(1)
xy.copy_within(0..n - 1, 1);
// Store x0 x0 x1 x2 y1 y2
xy[0] = x0;
// Compute y0 by multiply-accumulate
let y0 = if hold {
xy[n / 2 + 1]
} else {
macc(self.y_offset, xy, &self.ba)
};
// Limit y0
let y0 = max(self.y_min, min(self.y_max, y0));
// Store y0 x0 x1 y0 y1 y2
xy[n / 2] = y0;
y0
}
}