buttord function

Butterworth filter order and cutoff frequency

Compute the minimum filter order of a Butterworth filter with the desired response characteristics.

buttord(Wp, Ws, Rp, Rs, plane = c("z", "s"))

Arguments

• Wp, Ws: pass-band and stop-band edges. For a low-pass or high-pass filter, Wp and Ws are scalars. For a band-pass or band-rejection filter, both are vectors of length 2. For a low-pass filter, Wp < Ws. For a high-pass filter, Ws > Wp. For a band-pass (Ws[1] < Wp[1] < Wp[2] < Ws[2]) or band-reject (Wp[1] < Ws[1] < Ws[2] < Wp[2]) filter design, Wp gives the edges of the pass band, and Ws gives the edges of the stop band. For digital filters, frequencies are normalized to [0, 1], corresponding to the range [0, fs/2]. In case of an analog filter, all frequencies are specified in radians per second.
• Rp: allowable decibels of ripple in the pass band.
• Rs: minimum attenuation in the stop band in dB.
• plane: "z" for a digital filter or "s" for an analog filter.

Returns

A list of class FilterSpecs with the following list elements:

• n: filter order
• Wc: cutoff frequency
• type: filter type, normally one of "low", "high", "stop", or "pass".

Details

Deriving the order and cutoff is based on:

With some algebra, you can solve simultaneously for Wc and N

given Ws, Rs and Wp,Rp. Rounding N to the next greater integer, one can recalculate the allowable range for Wc (filter characteristic touching the pass band edge or the stop band edge).

For other types of filter, before making the above calculation, the requirements must be transformed to lowpass requirements. After the calculation, Wc must be transformed back to the original filter type.

Examples

## low-pass 30 Hz filter
fs <- 128
butspec <- buttord(30/(fs/2), 40/(fs/2), 0.5, 40)
but <- butter(butspec)
freqz(but, fs = fs)

See Also

butter, FilterSpecs

Author(s)

Paul Kienzle,

adapted by Charles Praplan.

Conversion to R by Tom Short,

adapted by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .