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#' Perform Method of Finite Differences Over One Column
#'
#' @param x raw data to be differentiated
#' @param S sample rate of data to return derivatives using raw time
#' @return first-order numerical derivatives estimated from data
.packageName <- 'sindyr'
# S = unit of time across samples
finite_difference = function(x, S) {
n = length(x)
fdx <- vector(length = n)
fdx[1] = (x[2]-x[1])/S # first derivative
for (i in 3:(n-1)) {
fdx[i-2] = (x[i] - x[i-2]) / (2*S) # the intermediate ones
}
fdx[n] = (x[n] - x[n - 1]) / S # the last one
return(fdx) # exchange envelopes
}
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