buttord {signal} | R Documentation |
Compute butterworth filter order and cutoff for the desired response characteristics.
buttord(Wp, Ws, Rp, Rs)
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. Frequencies are normalized to [0,1],
corresponding to the range [0, Fs/2]. |
Rp |
allowable decibels of ripple in the pass band. |
Rs |
minimum attenuation in the stop band in dB. |
Deriving the order and cutoff is based on:
|H(W)|^2 = 1 / [1+(W/Wc)^(2n)] = 10^(-R/10)
With some algebra, you can solve simultaneously for Wc
and n
given
Ws
, Rs
and Wp
, Rp
. For high-pass filters, subtracting the band edges
from Fs/2, performing the test, and swapping the resulting Wc
back
works beautifully. For bandpass- and bandstop-filters, this process
significantly overdesigns. Artificially dividing n
by 2 in this case
helps a lot, but it still overdesigns.
An object of class FilterOfOrder
with the following list elements:
n |
filter order |
Wc |
cutoff frequency |
type |
filter type, one of "low", "high", "stop", or "pass" |
This object can be passed directly to butter
to compute filter coefficients.
Original Octave version by Paul Kienzle, pkienzle@user.sf.net. Conversion to R by Tom Short.
Octave Forge http://octave.sf.net
butter
, FilterOfOrder
, cheb1ord
Fs = 10000 btord = buttord(1000/(Fs/2), 1200/(Fs/2), 0.5, 29) plot(c(0, 1000, 1000, 0, 0), c(0, 0, -0.5, -0.5, 0), type = "l", xlab = "Frequency (Hz)", ylab = "Attenuation (dB)") bt = butter(btord) plot(c(0, 1000, 1000, 0, 0), c(0, 0, -0.5, -0.5, 0), type = "l", xlab = "Frequency (Hz)", ylab = "Attenuation (dB)", col = "red", ylim = c(-10,0), xlim = c(0,2000)) hf = freqz(bt, Fs = Fs) lines(hf$f, 20*log10(abs(hf$h)))