An algorithm for computing the Nth roots of unity in bit-reversed order

Abstract

Many versions of the fast Fourier transform require that the user provide a table of the Nth roots of unity arranged in bit-reversed order. An algorithm for creating this table is given in this paper. The algorithm uses approximately N complex multiplications for a time series of length N. The algorithm's main advantage is its insensitivity to computational errors. The cumulative roundoff error is proportional to \log_{2} N . Additionally, the algorithm can be easily implemented in a high-level computer language.