I'm confused. If you have a table of data where one of the columns varies from -A to A, what is the difficulty in calculating the odd and even parts by just adding (resp. subtracting) the values at x and -x and dividing by two? Even if you don't have a precisely symmetric span of x values you can use simple interpolation as long as your data points are reasonably dense.
Fourier analysis seems to be overkill in this case, unless I'm missing something.
Fourier analysis seems to be overkill in this case, unless I'm missing something.