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
`0` s (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")

[Package *stats* version 2.2.1 Index]