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# fracshift.R
# Copyright (C) 2020 Geert van Boxtel <gjmvanboxtel@gmail.com>
# Original Octave code:
# Copyright (C) 2008 Eric Chassande-Mottin, CNRS (France)
# Copyright (C) 2018 Juan Pablo Carbajal
#
# 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
# 20201122 GvB setup for gsignal v0.1.0
#------------------------------------------------------------------------------
#' Fractional shift
#'
#' Shift a signal by a (possibly fractional) number of samples.
#'
#' The function calculates the initial index and end index of the sequences of
#' 1’s in the rows of \code{x}. The clusters are sought in the rows of the array
#' \code{x}. The function works by finding the indexes of jumps between
#' consecutive values in the rows of \code{x}.
#'
#' @param x input data, specified as a numeric vector.
#' @param d number of samples to shift \code{x} by, specified as a numeric value
#' @param h interpolator impulse response, specified as a numeric vector. If
#' NULL (default), the interpolator is designed by a Kaiser-windowed sinecard.
#'
#' @return A list of matrices size \code{nr}, where \code{nr} is the number of
#' rows in \code{x}. Each element of the list contains a matrix with two rows.
#' The first row is the initial index of a sequence of 1s and the second row
#' is the end index of that sequence. If \code{nr == 1} the output is a matrix
#' with two rows.
#'
#' @examples
#' N = 1024
#' t <- seq(0, 1, length.out = N)
#' x <- exp(-t^2 / 2 / 0.25^2) * sin(2 * pi * 10 * t)
#' dt <- 0.25
#' d <- dt / (t[2] - t[1])
#' y <- fracshift(x, d)
#' plot(t, x, type = "l", xlab = "Time", ylab = "Sigfnal")
#' lines (t, y, col = "red")
#' legend("topright", legend = c("original", "shifted"), lty = 1, col = 1:2)
#'
#' @author Eric Chassande-Mottin, \email{ecm@@apc.univ-paris7.fr},\cr
#' Juan Pablo Carbajal, \email{carbajal@@ifi.uzh.ch},\cr
#' Conversion to R by Geert van Boxtel, \email{G.J.M.vanBoxtel@@gmail.com}.
#'
#' @references [1] A. V. Oppenheim, R. W. Schafer and J. R. Buck,
#' Discrete-time signal processing, Signal processing series,
#' Prentice-Hall, 1999.\cr
#' [2] T.I. Laakso, V. Valimaki, M. Karjalainen and U.K. Laine
#' Splitting the unit delay, IEEE Signal Processing Magazine,
#' vol. 13, no. 1, pp 30--59 Jan 1996.
#
#' @export
fracshift <- function(x, d, h = NULL) {
if (!is.vector(x) || !is.numeric(x)) {
stop("x must be a numeric vector")
}
if (!isScalar(d)) {
stop("d must be a scalar")
}
if (!is.null(h)) {
if (!is.numeric(h) || !is.vector(h)) {
stop("h must be a numeric vector")
}
} else {
h <- design_filter(d)
Lx <- length(x)
Lh <- length(h)
L <- (Lh - 1) / 2.0
Ly <- Lx
## pre and postpad filter response
hpad <- prepad(h, Lh)
offset <- floor(L)
hpad <- postpad(hpad, Ly + offset)
## filtering
xfilt <- upfirdn(x, hpad, 1, 1)
x <- xfilt[(offset + 1):(offset + Ly)]
}
y <- pracma::circshift(x, trunc(d))
y
}
design_filter <- function(d) {
## properties of the interpolation filter
log10_rejection <- -3.0
## use empirical formula from [1] Chap 7, Eq. (7.63) p 476
rejection_dB <- -20.0 * log10_rejection
## determine parameter of Kaiser window
## use empirical formula from [1] Chap 7, Eq. (7.62) p 474
## FIXME since the parameters are fix the conditional below is not needed
if (rejection_dB >= 21 && rejection_dB <= 50) {
beta <- 0.5842 * (rejection_dB - 21.0)^0.4 + 0.07886 * (rejection_dB - 21.0)
} else if (rejection_dB > 50) {
beta <- 0.1102 * (rejection_dB - 8.7)
} else {
beta <- 0.0
}
## properties of the interpolation filter
stopband_cutoff_f <- 0.5
roll_off_width <- stopband_cutoff_f / 10
## ideal sinc filter
## determine filter length
L <- ceiling((rejection_dB - 8.0) / (28.714 * roll_off_width))
t <- (-L:L)
ideal_filter <- 2 * stopband_cutoff_f *
sinc(2 * stopband_cutoff_f * (t - (d - trunc(d))))
## apodize ideal (sincard) filter response
m <- 2 * L
t <- (0:m) - (d - trunc(d))
# kludge to prevent sqrt of negative number
# besselI does not take complex input
qq <- t * (m - t)
qq[which(qq < 0)] <- 0
t <- 2 * beta / m * sqrt(qq)
w <- besselI(t, 0) / besselI(beta, 0)
h <- w * ideal_filter
h
}
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