Design an 'IIR' filter

Usage

design_filter_iir(
  method = c("butter", "cheby1", "cheby2", "ellip"),
  sample_rate,
  filter_order = NA,
  use_sos = TRUE,
  high_pass_freq = NA,
  high_pass_trans_freq = NA,
  low_pass_freq = NA,
  low_pass_trans_freq = NA,
  passband_ripple = 0.1,
  stopband_attenuation = 40
)

Arguments

method: filter method name, choices are "butter", "cheby1", "cheby2", and "ellip"
sample_rate: sampling frequency
filter_order: suggested filter order. When use_sos=TRUE (default) this order is used as-is since 'SOS' form is numerically stable at any order. When use_sos=FALSE and 'ARMA' form becomes numerically unstable, the order will be automatically reduced with a warning; leave NA (default) to let the function choose automatically.
use_sos: logical; when TRUE (default), the filter is also stored as a Sos (second-order sections) object in filter$sos, and no stability-based order correction is performed. When FALSE, the order is capped at the maximum stable 'ARMA' order (with a warning if a specific filter_order was requested).
high_pass_freq: high-pass frequency; default is NA (no high-pass filter will be applied)
high_pass_trans_freq: high-pass frequency band-width; default is automatically inferred from filter type.
low_pass_freq: low-pass frequency; default is NA (no low-pass filter will be applied)
low_pass_trans_freq: low-pass frequency band-width; default is automatically inferred from filter type.
passband_ripple: allowable pass-band ripple in decibel; default is 0.1
stopband_attenuation: minimum stop-band attenuation (in decibel) at transition frequency; default is 40 dB.

Value

A filter object with $b/$a 'ARMA' coefficients and $sos second-order sections (a gsignal Sos object).

Examples


sample_rate <- 500

my_diagnose <- function(
    filter, vlines = c(8, 12), cutoffs = c(-3, -6)) {
  diagnose_filter(
    b = filter$b,
    a = filter$a,
    fs = sample_rate,
    vlines = vlines,
    cutoffs = cutoffs
  )
}

# ---- Default using butterworth to generate 8-12 bandpass filter ----

# Butterworth filter with cut-off frequency
# 7 ~ 13 (default transition bandwidth is 1Hz) at -3 dB
filter <- design_filter_iir(
  method = "butter",
  low_pass_freq = 12,
  high_pass_freq = 8,
  sample_rate = 500
)

filter
#> <IIR filter>
#>   Type : pass
#>   Method: butter
#>   Order: 9
#>   Magnitude:
#>     Freq=8 Hz, mag=-175.2 dB (expected=-0.1 dB)
#>     Freq=12 Hz, mag=-146.5 dB (expected=-0.1 dB)
#>     Freq=6 Hz, mag=-198.9 dB (expected=-40 dB)
#>     Freq=15 Hz, mag=-124.6 dB (expected=-40 dB)
#>   Reciprocal condition number: 2.7e-22 < .Machine$double.eps
#>   
#>   WARNING: 
#>    * Unstable autoregressive (AR) polynomial coefficients

my_diagnose(filter)


## explicit bandwidths and attenuation (sharper transition)

# Butterworth filter with cut-off frequency
# passband ripple is 0.5 dB (8-12 Hz)
# stopband attenuation is 40 dB (5-18 Hz)
filter <- design_filter_iir(
  method = "butter",
  low_pass_freq = 12, low_pass_trans_freq = 6,
  high_pass_freq = 8, high_pass_trans_freq = 3,
  sample_rate = 500,
  passband_ripple = 0.5,
  stopband_attenuation = 40
)

filter
#> <IIR filter>
#>   Type : pass
#>   Method: butter
#>   Order: 5
#>   Magnitude:
#>     Freq=8 Hz, mag=-0.5076 dB (expected=-0.5 dB)
#>     Freq=12 Hz, mag=-0.5011 dB (expected=-0.5 dB)
#>     Freq=5 Hz, mag=-45.85 dB (expected=-40 dB)
#>     Freq=18 Hz, mag=-41.04 dB (expected=-40 dB)
#>   Reciprocal condition number: 1.7e-15 > .Machine$double.eps

my_diagnose(filter)


# ---- cheby1 --------------------------------

filter <- design_filter_iir(
  method = "cheby1",
  low_pass_freq = 12,
  high_pass_freq = 8,
  sample_rate = 500
)

my_diagnose(filter)


# ---- cheby2 --------------------------------

filter <- design_filter_iir(
  method = "cheby2",
  low_pass_freq = 12,
  high_pass_freq = 8,
  sample_rate = 500
)

my_diagnose(filter)


# ----- ellip ---------------------------------

filter <- design_filter_iir(
  method = "ellip",
  low_pass_freq = 12,
  high_pass_freq = 8,
  sample_rate = 500
)

my_diagnose(filter)