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## Copyright (C) 1999 Paul Kienzle
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## Generate an Chebyshev type I filter with Rp dB of pass band ripple.
##
## [b, a] = cheby1(n, Rp, Wc)
## low pass filter with cutoff pi*Wc radians
##
## [b, a] = cheby1(n, Rp, Wc, 'high')
## high pass filter with cutoff pi*Wc radians
##
## [b, a] = cheby1(n, Rp, [Wl, Wh])
## band pass filter with edges pi*Wl and pi*Wh radians
##
## [b, a] = cheby1(n, Rp, [Wl, Wh], 'stop')
## band reject filter with edges pi*Wl and pi*Wh radians
##
## [z, p, g] = cheby1(...)
## return filter as zero-pole-gain rather than coefficients of the
## numerator and denominator polynomials.
##
## [...] = cheby1(...,'s')
## return a Laplace space filter, W can be larger than 1.
##
## [a,b,c,d] = cheby1(...)
## return state-space matrices
##
## References:
##
## Parks & Burrus (1987). Digital Filter Design. New York:
## John Wiley & Sons, Inc.
## Author: Paul Kienzle <pkienzle@user.sf.net>
## Modified: Doug Stewart Feb. 2003
cheby1 <- function(n, ...) UseMethod("cheby1")
cheby1.FilterOfOrder <- function(n, Rp = n$Rp, W = n$Wc, type = n$type, ...)
cheby1(n$n, Rp, W, type, ...)
cheby1.default <- function(n, Rp, W, type = c("low", "high", "stop", "pass"), plane = c("z", "s"), ...) {
type <- match.arg(type)
plane <- match.arg(plane)
## interpret the input parameters
if (!(length(n)==1 && n == round(n) && n > 0))
stop("cheby1: filter order n must be a positive integer")
stop <- type == "stop" || type == "high"
digital <- plane == "z"
if (length(W) != 1 && length(W) != 2)
stop("cheby1: frequency must be given as w0 or c(w0, w1)")
if (digital && !all(W >= 0 & W <= 1))
stop("cheby1: critical frequencies must be in (0 1)")
else if (!digital && !all(W >= 0))
stop("cheby1: critical frequencies must be in (0 inf)")
if (Rp < 0)
stop("cheby1: passband ripple must be positive decibels")
## Prewarp to the band edges to s plane
if (digital) {
T <- 2 # sampling frequency of 2 Hz
W <- 2 / T*tan(pi * W / T)
}
## Generate splane poles and zeros for the chebyshev type 1 filter
epsilon <- sqrt(10^(Rp/10) - 1)
v0 <- asinh(1/epsilon)/n
pole <- exp(1i*pi*c(seq(-(n-1), (n-1), by = 2))/(2*n))
pole <- -sinh(v0)*Re(pole) + 1i*cosh(v0)*Im(pole)
zero <- numeric(0)
## compensate for amplitude at s=0
gain <- prod(-pole)
## if n is even, the ripple starts low, but if n is odd the ripple
## starts high. We must adjust the s=0 amplitude to compensate.
if (n %% 2 == 0)
gain <- gain/10^(Rp/20)
ZPG <- Zpg(zero = zero, pole = pole, gain = gain)
## s-plane frequency transform
ZPG <- sftrans(ZPG, W = W, stop = stop)
## Use bilinear transform to convert poles to the z plane
if (digital)
ZPG <- bilinear(ZPG, T = T)
as.Arma(ZPG)
}
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