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### This function is a component of astrochron: An R Package for Astrochronology
### Copyright (C) 2021 Huaran Liu and Stephen Meyers
#' Convolution through Fast Fouriem Transform
#'
#' x and y do not need to be of the same length.
#'
#' @param x Input signal that needs to be convolved.
#' @param y Green function/ Impulse response function.
#' @param dt time resolution for the input series
#' @param index index in the impulse response function that corresponds to the deposition time
#' @return z Convolved output series. length(z) = length(x)
#' @import stats
#' @export
conv_fft <- function(x, y, index, dt){
# Pad input series with 0 to the length of length(x)+length(y)-1
nx <- length(x)
ny <- length(y)
nfft <- nx+ny-1
x <- append(x, rep(0, ny-1))
y <- append(y, rep(0, nx-1))
fft_z <- Re(fft( fft(x)*fft(y), inverse = TRUE)/nfft)
z <- fft_z[index: (nfft-(ny-index))]*dt
return(z)
}
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