flaw

Control-law-inspired embedded signal filtering, no-std and no-alloc compatible.

This library provides a simple method for initializing and updating single-input, single-output infinite-impulse-response filters using 32-bit floats, as well as tabulated filter coefficients for some common filters. Filters evaluate in 4N+1 floating-point operations for a filter of order N.

The name flaw is short for filter-law, but also refers to the fact that digital IIR filtering with small floating-point types is an inherently flawed approach, in that higher-order and lower-cutoff filters produce very small coefficients that result in floating-point roundoff error. This library makes an attempt to mitigate this problem by providing filter coefficients for a tested domain of validity. The result is a limited, but useful, range of operation where these filters can achieve both accuracy and performance as well as be formulated and initialized in an embedded environment.

Example: Second-Order Butterworth Filter

// First, choose a cutoff frequency as a fraction of sampling frequency
let cutoff_ratio = 1e-3;

// Initialize a filter, interpolating coefficients to that cutoff ratio.
let mut filter = flaw::butter2(cutoff_ratio).unwrap();  // Errors if extrapolating

// Update the filter with a new raw measurement
let measurement = 0.3145; // Some number
let estimate = filter.update(measurement);  // Latest state estimate

Development Status: Early Days

This is in an experimental stage - it appears to work well, but is not fully-validated or fully-featured.

• More software testing is needed to guarantee filter performance at interpolated cutoff ratios
• More hardware/firmware testing is needed to examine performance on actual microcontrollers
• More filter types can be added

Coefficient Tables

Tabulated filters are tested to enforce

• <0.1% error in converged step response at the minimum cutoff frequency
• <1ppm error in converged step response at the maximum cutoff frequency
• <5% error to -3dB attenuation of a sine input at the cutoff frequency at the maximum cutoff ratio
  • This error appears to be mainly an issue of discretization in test cases, and could be reduced by using a better method for testing (fit a sine curve to the result or do gradient-descent on a cubic interpolator)

Each filter with tabulated coefficients has a minimum and maximum cutoff ratio. The minimum value is determined by floating-point error in convergence of a step response, while the maximum value is determined by the accuracy of attenuation at the cutoff frequency as the cutoff ratio approaches the Nyquist frequency.

Coefficients for a given filter are interpolated on these tables using a cubic Hermite method with the log10(cutoff_ratio) as the independent variable. Tabulated values are stored and interpolated as 64-bit floats, and only converted to 32-bit floats at the final stage of calculation.

Filter coefficients are extracted from scipy's state-space representations, which are the result of a bilinear transform of the transfer function polynomials.

License

Licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.