Causal and stateful IIR filtering primitives

This file provides one-pass, causal, state-carrying IIR filtering that mirrors scipy.signal (lfilter, lfilter_zi, sosfilt, sosfilt_zi, sosfiltfilt). Unlike the zero-phase butterworthFilter default (which uses forward-backward filtfilt and is inherently non-causal), these functions process a signal strictly forward in time and can carry filter state across consecutive chunks. This is the numerical core that a real-time streaming backend (e.g. a future PhysioStream) reuses so that offline and online filtering produce identical results.

Details

All recursions use the Direct-Form-II-Transposed (DF2T) structure, which is the same structure scipy.signal and signal::filter use, so the outputs agree to machine precision.

References

Oppenheim, A.V. & Schafer, R.W. (2010). Discrete-Time Signal Processing, 3rd ed. Prentice Hall.

Virtanen, P. et al. (2020). SciPy 1.0. Nature Methods 17, 261-272. (reference implementation: scipy.signal.sosfilt / lfilter / lfilter_zi / sosfilt_zi).