| convolve {stats} | R Documentation |
Use the Fast Fourier Transform to compute the several kinds of convolutions of two sequences.
convolve(x, y, conj = TRUE, type = c("circular", "open", "filter"))
x,y |
numeric sequences of the same length to be convolved. |
conj |
logical; if TRUE, take the complex conjugate
before back-transforming (default, and used for usual convolution). |
type |
character; one of "circular", "open",
"filter" (beginning of word is ok). For circular, the
two sequences are treated as circular, i.e., periodic.
For open and filter, the sequences are padded with
0s (from left and right) first; "filter" returns the
middle sub-vector of "open", namely, the result of running a
weighted mean of x with weights y. |
The Fast Fourier Transform, fft, is used for efficiency.
The input sequences x and y must have the same length if
circular is true.
Note that the usual definition of convolution of two sequences
x and y is given by convolve(x, rev(y), type = "o").
If r <- convolve(x,y, type = "open")
and n <- length(x), m <- length(y), then
r[k] = sum(i; x[k-m+i] * y[i])
where the sum is over all valid indices i, for k = 1,..., n+m-1
If type == "circular", n = m is required, and the above is
true for i , k = 1,...,n when
x[j] := x[n+j] for j < 1.
Brillinger, D. R. (1981) Time Series: Data Analysis and Theory, Second Edition. San Francisco: Holden-Day.
fft, nextn, and particularly
filter (from the stats package) which may be
more appropriate.
x <- c(0,0,0,100,0,0,0)
y <- c(0,0,1, 2 ,1,0,0)/4
zapsmall(convolve(x,y)) # *NOT* what you first thought.
zapsmall(convolve(x, y[3:5], type="f")) # rather
x <- rnorm(50)
y <- rnorm(50)
# Circular convolution *has* this symmetry:
all.equal(convolve(x,y, conj = FALSE), rev(convolve(rev(y),x)))
n <- length(x <- -20:24)
y <- (x-10)^2/1000 + rnorm(x)/8
Han <- function(y) # Hanning
convolve(y, c(1,2,1)/4, type = "filter")
plot(x,y, main="Using convolve(.) for Hanning filters")
lines(x[-c(1 , n) ], Han(y), col="red")
lines(x[-c(1:2, (n-1):n)], Han(Han(y)), lwd=2, col="dark blue")