fixed-filters

Biquad filters for fixed-point numbers.

fixed-filters is a #![no_std] library for creating biquad filters. These are simple 2nd order IIR filters which can be configured to implement a variety of filter behaviors (i.e. lowpass, bandpass, highpass, notch, proportional-integral, etc). It is designed specifically to work with 32-bit fixed-point numbers based on the fixed crate.

Alpha: This crate requires the alpha release of 2.0.0 of the fixed crate that makes use of const generics instead of the typenum crate. This version requires the nightly compiler with the [generic_const_exprs feature] enabled.

How to use

The main data structure for this crate is Biquad<X,Y> where X and Y are i32 constant generics which represent the number of fractional bits of the input and output signals respectively. While the run functions are all designed use fixed-point arithmetic, the construction APIs accept floating point variables to simplify use. The most generic way of creating a filter is to construct with new() and pass the filter coefficients.

#![feature(generic_const_exprs)]

use fixed_filters::Biquad;
use fixed::FixedI32;

// poles
let a0 = 1.;
let a1 = -1.97985135;
let a2 = 0.980052318;

// zeros
let b0 = 0.000050241;
let b1 = 0.000100482;
let b2 = 0.000050241;

// make a filter with 20 fractional bits on input and 16 fractional bits on output
let mut filter = Biquad::<20, 16>::new(a0, a1, a2, b0, b1, b2);

let signal = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0];
let mut y = FixedI32::<16>::ZERO;
for s in signal {
	let x = FixedI32::<20>::from_num(s); // convert to fixed-point number
	y = filter.update(x);
}

While passing the pole and zero coefficients is the most universal way of creating a filter, Biquad includes a number of associated functions for creating standard filter forms with the user specifying just the sampling period, the center frequency, and the q factor.

// create a butterworth lowpass filter
let ts = 1./10e3;
let f0 = 100.;
let q = core::f32::consts::FRAC_1_SQRT_2;
let mut filter = Biquad::<16, 16>::lowpass(ts, f0, q);

The library includes associted functions for creating the following filter forms:

1. lowpass
2. bandpass
3. highpass
4. notch
5. single_pole_lowpass
6. proportional-integral behavior

By default, the filters do not limit their output and can in fact over-flow if you are not careful. You can add limits to an existing filter using the set_min, set_max, or set_limit functions, or you can setup limits at construction using a builder pattern with the with_min, with_max, or with_limit functions.

// create a proportional-integral controller with a limit ot +-20
let kp = 0.1;
let ki = 0.01;
let mut filter = Biquad::<16, 16>::pi(kp, ki).with_limit(20.0);

Benchmarking

The performance of this crate was benchmarked against other available #![no_std] biquad filter implementations by running a filter at 10kHz in a simple RTIC application on an STM32F411RE Nucelo board. The RTIC monotonic API was used to quantify the number of CPU cycles used for each filters' update method.

From these results, it can be seen that the crates all provide similar performance in terms of execution efficiency with biquad DirectForm2Transposed having a slight edge in microcontrollers with an FPU. This crate however does not support internal limiting of the output signal which can be critical in certain applications such as implementing anti-windup and PI controllers.