butter: Butterworth filter design

Description

Compute the transfer function coefficients of a Butterworth filter.

Usage

butter(n, ...)
# S3 method for FilterSpecs
butter(n, ...)
# S3 method for default
butter(
  n,
  w,
  type = c("low", "high", "stop", "pass"),
  plane = c("z", "s"),
  output = c("Arma", "Zpg", "Sos"),
  ...
)

Value

Depending on the value of the output parameter, a list of class Arma, Zpg, or Sos

containing the filter coefficients

Arguments

n

filter order.

...

additional arguments passed to butter, overriding those given by n of class FilterSpecs.

w

critical frequencies of the filter. w must be a scalar for low-pass and high-pass filters, and w must be a two-element vector c(low, high) specifying the lower and upper bands in radians/second. For digital filters, w must be between 0 and 1 where 1 is the Nyquist frequency.

type

filter type, one of "low", (default) "high", "stop", or "pass".

plane

"z" for a digital filter or "s" for an analog filter.

output

Type of output, one of:

"Arma": Autoregressive-Moving average (aka numerator/denominator, aka b/a)

"Zpg"

Zero-pole-gain format

"Sos"

Second-order sections

Default is "Arma" for compatibility with the 'signal' package and the 'Matlab' and 'Octave' equivalents, but "Sos" should be preferred for general-purpose filtering because of numeric stability.

Author

Paul Kienzle, pkienzle@users.sf.net,
Doug Stewart, dastew@sympatico.ca,
Alexander Klein, alexander.klein@math.uni-giessen.de,
John W. Eaton.
Conversion to R by Tom Short,
adapted by Geert van Boxtel G.J.M.vanBoxtel@gmail.com.

Details

Butterworth filters have a magnitude response that is maximally flat in the passband and monotonic overall. This smoothness comes at the price of decreased rolloff steepness. Elliptic and Chebyshev filters generally provide steeper rolloff for a given filter order.

Because butter is generic, it can be extended to accept other inputs, using buttord to generate filter criteria for example.

References

https://en.wikipedia.org/wiki/Butterworth_filter

Examples

Run this code

## 50 Hz notch filter
fs <- 256
bf <- butter(4, c(48, 52) / (fs / 2), "stop")
freqz(bf, fs = fs)

## EEG alpha rhythm (8 - 12 Hz) bandpass filter
fs <- 128
fpass <- c(8, 12)
wpass <- fpass / (fs / 2)
but <- butter(5, wpass, "pass")
freqz(but, fs = fs)

## filter to remove vocals from songs, 25 dB attenuation in stop band
## (not optimal with a Butterworth filter)
fs <- 44100
specs <- buttord(230/(fs/2), 450/(fs/2), 1, 25)
bf <- butter(specs)
freqz(bf, fs = fs)
zplane(bf)

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