# fwht.R
# Copyright (C) 2020 Geert van Boxtel <gjmvanboxtel@gmail.com>
# Original Octave code:
# Copyright (C) 2013-2019 Mike Miller
#
# 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
# 20201023 GvB setup for gsignal v0.1.0
#------------------------------------------------------------------------------
#' Fast Walsh-Hadamard Transform
#'
#' Compute the (inverse) Fast Walsh-Hadamard transform of a signal.
#'
#' @param x input data, specified as a numeric vector or matrix. In case of a
#' vector it represents a single signal; in case of a matrix each column is a
#' signal. \code{fwht} operates only on signals with length equal to a power
#' of 2. If the length of \code{x} is less than a power of 2, its length is
#' padded with zeros to the next greater power of two before processing.
#' @param n transform length, specified as a positive integer scalar. Default:
#' \code{NROW(x)}.
#' @param ordering order of the Walsh-Hadamard transform coefficients, one of:
#' \describe{
#' \item{"sequency"}{(Default) Coefficients in order of increasing sequency
#' value, where each row has an additional zero crossing.}
#' \item{"hadamard"}{Coefficients in normal Hadamard order}
#' \item{"dyadic"}{Coefficients in Gray code order, where a single bit change
#' occurs from one coefficient to the next}
#' }
#'
#' @return (Inverse) Fast Walsh Hadamard transform, returned as a vector or
#' matrix.
#'
#' @examples
#' x <- c(19, -1, 11, -9, -7, 13, -15, 5)
#' X <- fwht(x)
#' all.equal(x, ifwht(X))
#'
#' @author Mike Miller.\cr
#' Conversion to R by Geert van Boxtel, \email{G.J.M.vanBoxtel@@gmail.com}.
#'
#' @references \url{https://en.wikipedia.org/wiki/Hadamard_transform}
#' @references \url{https://en.wikipedia.org/wiki/Fast_Walsh-Hadamard_transform}
#'
#' @rdname fwht
#' @export
ifwht <- function(x, n = NROW(x),
ordering = c("sequency", "hadamard", "dyadic")) {
# check parameters
if (!(is.vector(x) || is.matrix(x)) || !is.numeric(x)) {
stop("x must be a numeric or vector or matrix")
}
if (is.vector(x)) {
vec <- TRUE
x <- as.matrix(x, ncol = 1)
} else {
vec <- FALSE
}
nr <- nrow(x)
if (!isPosscal(n) || !isWhole(n)) {
stop("n must be a positive integer")
}
# force n to be a power of 2
n <- nextpow2(n)
if (n != nr) {
x <- postpad(x, n)
}
ordering <- match.arg(ordering)
# Zero-based index for normal Hadamard ordering
idx <- seq(0, n - 1)
nbits <- floor(log2(max(idx))) + 1 # number of significant bits
# Gray code permutation of index for alternate orderings
idx_bin <- matrix(0, n, nbits)
if (ordering == "dyadic") {
for (i in seq_len(n)) {
idx_bin[i, ] <- as.integer(intToBits(idx[i]))[1:nbits]
idx[i] <- bin2dec(paste(idx_bin[i, ], collapse = "")) + 1
}
} else if (ordering == "sequency") {
for (i in seq_len(n)) {
idx_bin[i, ] <- as.integer(rev(intToBits(idx[i])))[(32 - nbits + 1):32]
idx_bin_a <- idx_bin[i, 1:(nbits - 1)]
idx_bin_b <- idx_bin[i, 2:nbits]
idx_bin[i, 2:nbits] <- (idx_bin_a + idx_bin_b) %% 2
idx[i] <- bin2dec(paste(rev(idx_bin[i, ]), collapse = "")) + 1
}
} else {
idx <- idx + 1
}
# do the transform
if (n < 2) {
y <- x
} else {
y <- .Call("_gsignal_fwht", PACKAGE = "gsignal", x)
}
# apply ordering
y <- y[idx, ]
# cleanup and exit
if (vec) {
y <- as.vector(y)
}
y
}
#' @rdname fwht
#' @export
fwht <- function(x, n = NROW(x),
ordering = c("sequency", "hadamard", "dyadic")) {
if (!isPosscal(n) || !isWhole(n)) {
stop("n must be a positive integer")
}
n <- nextpow2(n)
y <- ifwht(x, n, ordering)
y <- y / n
y
}
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