Butterworth bandpass filter — bandpass

Design and apply a zero-phase Butterworth bandpass filter to a signal, using scipy-compatible steady-state initial conditions (equivalent to scipy.signal.sosfiltfilt / scipy.signal.filtfilt with padtype = "odd").

Usage

bandpass_filter(x, flp, fhi, delt, order = 2)

Arguments

x: Numeric vector. Signal to be filtered.
flp: Numeric. Low-pass cutoff frequency (Hz).
fhi: Numeric. High-pass cutoff frequency (Hz).
delt: Numeric. Sampling interval in seconds (i.e. TR for fMRI).
order: Integer. Filter order. Default is 2.

Value

Numeric vector. Zero-phase filtered signal, same length as x.

Details

Two internal code paths are used depending on order:

order <= 3 (typical fMRI use): direct-form b/a coefficients with the companion-matrix initial-condition method. scipy filtfilt-parity validated to < 1e-9 for standard fMRI parameters.
order >= 4: second-order sections (SOS). The companion matrix for the full-order b/a representation becomes ill-conditioned for high-order filters with poles close to z = 1 (very low lower cutoff). SOS avoids this by decomposing the filter into biquad sections, each with a 2x2 companion matrix that is always well-conditioned.

Filter coefficients are computed by .butter_bandpass_zpk(), a bespoke port of scipy.signal.butter() that requires no external packages.

Examples

set.seed(1)
x <- rnorm(200)
x_filt <- bandpass_filter(x, flp = 0.01, fhi = 0.1, delt = 2, order = 2)