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 |
fft, is used for efficiency.
The input sequences x and y must have the same length if
circular = TRUE).
r <- convolve(x,y, conj=TRUE, type)
and n <- length(x), then
r[k] = sum(i=1,..,n; x[i] * y[k-i])
for k = 1,...,n.
If type == "circular", then
y[j] == y[n+j] for j < 0.
fft, nextn.
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)
all(convolve(x,y), convolve(y,x))
all(convolve(x,y, conj = FALSE), rev(convolve(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")