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 (1977). To reduce memory requirements, when *n* is small, the Fourier coefficients are computed directly using the defining formulas.