'Butterworth' filter with maximum order — butter_max

Large filter order might not be optimal, but at lease this function provides a feasible upper bound for the order such that the filter has a stable AR component.

Usage

butter_max_order(
  w,
  type = c("low", "high", "pass", "stop"),
  r = 10 * log10(2),
  tol = .Machine$double.eps
)

Arguments

w: scaled frequency ranging from 0 to 1, where 1 is 'Nyquist' frequency
type: filter type
r: decibel attenuation at frequency w, default is around 3 dB (half power)
tol: tolerance of reciprocal condition number, default is .Machine$double.eps.

Value

'Butterworth' filter in 'Arma' form.

Examples


# Find highest order (sharpest transition) of a band-pass filter
sample_rate <- 500
nyquist <- sample_rate / 2

type <- "pass"
w <- c(1, 50) / nyquist
Rs <- 6     # power attenuation at w

# max order filter
filter <- butter_max_order(w, "pass", Rs)

# -6 dB cutoff should be around 1 ~ 50 Hz
diagnose_filter(filter$b, filter$a, fs = sample_rate)