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(log₂ N) additions and O(log₂ N) multiplications per harmonic. In this paper, an improvement is proposed by which any harmonic can be calculated at a cost of O(log₂ N) additions but only two complex multiplications. The new technique stems from the application of the frequency-shifting property to existing methods