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Rev 69587 Rev 69588
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}
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}
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\usage{
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\usage{
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convolve(x, y, conj = TRUE, type = c("circular", "open", "filter"))
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convolve(x, y, conj = TRUE, type = c("circular", "open", "filter"))
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}
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}
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\arguments{
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\arguments{
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  \item{x, y}{numeric sequences to be convolved, \emph{of the same
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  \item{x, y}{numeric sequences \emph{of the same length} to be
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      length} for \code{type = "circular"}, the default.  For \code{type
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      = "filter"}, \code{y} must not be longer than \code{y} (and
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    typically is much shorter).}
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    convolved.}
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  \item{conj}{logical; if \code{TRUE}, take the complex \emph{conjugate}
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  \item{conj}{logical; if \code{TRUE}, take the complex \emph{conjugate}
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    before back-transforming (default, and used for usual convolution).}
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    before back-transforming (default, and used for usual convolution).}
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  \item{type}{character; partially matched to \code{"circular"}, \code{"open"},
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  \item{type}{character; partially matched to \code{"circular"}, \code{"open"},
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    \code{"filter"}.  For \code{"circular"}, the
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    \code{"filter"}.  For \code{"circular"}, the
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    two sequences are treated as \emph{circular}, i.e., periodic.
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    two sequences are treated as \emph{circular}, i.e., periodic.
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x <- rnorm(50)
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x <- rnorm(50)
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y <- rnorm(50)
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y <- rnorm(50)
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# Circular convolution *has* this symmetry:
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# Circular convolution *has* this symmetry:
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all.equal(convolve(x, y, conj = FALSE), rev(convolve(rev(y),x)))
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all.equal(convolve(x, y, conj = FALSE), rev(convolve(rev(y),x)))
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(ctypes <- eval(formals(convolve)$type)[-1]) # all but "circular"
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for(n in 1:500) {%% <- FIXME ?  \dontshow{..} ??
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 x <- rnorm(1+ rpois(1, 20))
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 y <- rnorm(1+ rpois(1, sample(c(4,40), 1)))
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 Lxy <- sapply(ctypes, function(T) convolve(x,y, type=T), simplify=FALSE)
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 stopifnot(all.equal(Lxy$open,   Lxy$`1+open`,   tol=1e-14))
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 stopifnot(all.equal(Lxy$filter, Lxy$`1+filter`, tol=1e-14))
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}
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n <- length(x <- -20:24)
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n <- length(x <- -20:24)
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y <- (x-10)^2/1000 + rnorm(x)/8
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y <- (x-10)^2/1000 + rnorm(x)/8
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Han <- function(y) # Hanning
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Han <- function(y) # Hanning
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       convolve(y, c(1,2,1)/4, type = "filter")
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       convolve(y, c(1,2,1)/4, type = "filter")