# sos2zp.R
# Copyright (C) 2020 Geert van Boxtel <gjmvanboxtel@gmail.com>
# Original Octave version:
# Copyright (C) 2005 Julius O. Smith III <jos@ccrma.stanford.edu>
#
# 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 3
# 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, see <http://www.gnu.org/licenses/>.
#
# Version history
# 20200330 GvB setup for gsignal v0.1.0
# 20200405 GvB replaced roots() by pracma::roots()
# 20200406 GvB validated
# 20210326 GvB return object of class 'Zpg'
# 20210506 GvB use matrix() instead of as.matrix(), sort output
#------------------------------------------------------------------------------
#' Sos to zero-pole-gain
#'
#' Convert digital filter second-order section data to zero-pole-gain form.
#'
#' @param sos Second-order section representation, specified as an nrow-by-6
#' matrix, whose rows contain the numerator and denominator coefficients of
#' the second-order sections:\cr \code{sos <- rbind(cbind(B1, A1), cbind(...),
#' cbind(Bn, An))}, where \code{B1 <- c(b0, b1, b2)}, and \code{A1 <- c(a0,
#' a1, a2)} for section 1, etc. The b0 entry must be nonzero for each section.
#' @param g Overall gain factor that effectively scales the output \code{b}
#' vector (or any one of the input \code{B_i} vectors). Default: 1.
#'
#'@return A list of class "Zpg" with the following list elements:
#' \describe{
#' \item{z}{complex vector of the zeros of the model (roots of \code{B(z)})}
#' \item{p}{complex vector of the poles of the model (roots of \code{A(z)})}
#' \item{k}{overall gain (\code{B(Inf)})}
#' }
#'
#' @seealso \code{\link{filter}}
#'
#' @examples
#' sos <- rbind(c(1, 0, 1, 1, 0, -0.81), c(1, 0, 0, 1, 0, 0.49))
#' zpk <- sos2zp(sos)
#'
#' @author Julius O. Smith III \email{jos@@ccrma.stanford.edu}.\cr
#' Conversion to R by, Geert van Boxtel \email{G.J.M.vanBoxtel@@gmail.com}
#'
#' @export
sos2zp <- function(sos, g = 1) {
sos <- matrix(sos, ncol = 6)
n <- nrow(sos)
m <- ncol(sos)
if (m != 6) {
stop("sos must be a nrow-by-6 matrix")
}
gains <- sos[, 1] # All b0 coeffs
g <- prod(gains) * g # pole-zero gain
if (g == 0) {
stop("one or more section gains is zero")
}
sos[, 1:3] <- sos[, 1:3] / c(gains, gains, gains)
z <- p <- rep(0L, 2 * n)
for (i in seq_len(n)) {
ndx <- (2 * i - 1):(2 * i)
zi <- pracma::roots(sos[i, 1:3])
z[ndx] <- zi
pi <- pracma::roots(sos[i, 4:6])
p[ndx] <- pi
}
Zpg(z = sort(z), p = sort(p), g = g)
}
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