## Fast Convolution

## Usage

    convolve(x, y, conj = TRUE)

## Arguments

`x,y` | numeric sequences of the same length to be convolved.

## Value

This function uses the Fast Fourier Transform to compute the (circular) convolution of the sequences given as its arguments. If `r <- convolve(x,y)` and `n <- length(x)`, then

r[k] = sum(i=1,..,n; x[i] * y[k-i])

for k = 1,...,n, where y[j] == y[n+j] for j < 0.

The Fast Fourier Transform, `fft`, is used for efficiency.

## References

Brillinger, D. R. (1981). Time Series: Data Analysis and Theory, Second Edition. San Francisco: Holden-Day.

## See Also

`fft`, `nextn`.

## Examples

    x <- c(0,0,0,100,0,0,0)
    y <- c(0,0,1, 2 ,1,0,0)/4
    round(convolve(x,y), 7)# this is *NOT* what you first thought..
    x <- rnorm(50);y <- rnorm(50)
    all(convolve(x,y), convolve(y,x))
    all(convolve(x,y, conj = FALSE), rev(convolve(y,x)))

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