If the number of observations n factors into prime integers that are less than or equal to 23, and the product of the square-free factors of n is less than 210, then PROC SPECTRA uses the fast Fourier transform developed by Cooley and Tukey and implemented by Singleton (1969). If n cannot be factored in this way, then PROC SPECTRA uses a Chirp-Z algorithm similar to that proposed by Monro and Branch (1976). To reduce memory requirements, when n is small, the Fourier coefficients are computed directly using the defining formulas.