butter

Create a Butterworth filter.

Syntax

[b,a] = butter(n,Wp)

[b,a] = butter(n,Wp,band)

[b,a] = butter(n,Wp,domain)

[b,a] = butter(n,Wp,band,domain)

Inputs

n
The filter order.
Type: integer
Dimension: scalar
Wp
A scalar specifying the 3dB cutoff frequency of a low or high pass filter, or a two element vector specifying the cutoff frequencies of a bandpass or bandstop filter. For a digital filter the values (in Hz) are normalized relative to the Nyquist frequency. For an analog filter the values are in radians/sec.
Type: double
Dimension: scalar | vector
band
The band type of the filter. Omit for low pass or bandpass. Use 'high' for high pass, and 'stop' for bandstop.
Type: string
domain
Omit for digital filters. Use 's' for analog filters.
Type: string

Outputs

b
The numerator polynomial coefficients of the filter.
Type: vector
a
The denominator polynomial coefficients of the filter.
Type: vector

Example

Create a fourth order Butterworth low pass digital filter with a 300 Hz cutoff frequency and a 1000 Hz sampling frequency.

[b,a] = butter(4,300/500)
b = [ 0.16718 0.66872 1.0031 0.66872 0.16718 ]
a = [ 1 0.7821 0.67998 0.18268 0.030119 ]

Comments

The attenuation at Wp is 20*log10(sqrt(2)), or approximately 3.0103 dB.

Filters can become unstable for high orders, and more easily so for bandpass or stopband filters.