Fast non-recursive computation of individual running harmonics

It has been recently shown that the fast Fourier transform of a sequence which slides over a time-limited rectangular window can be carried out in a nonrecursive manner by means of O(N) computations. When only certain individual harmonics are needed, the application of this technique leads to O(log, N) additions and O(log, N) multiplications per harmonic. In this paper, an improvement is proposed by which any harmonic can be calculated at a cost of O(log, N) additions but only two complex multiplications. The nem technique stems from the application of the frequency-shifting property to existing methods.