On the use of symmetry in FFT computation

It is well known that if a finite duration, N-point sequence x(n) possesses certain symmetries, the computation of its discrete Fourier transform (DFT) can be obtained from an FFT of size N/2 or smaller. This is accomplished by first preprocessing the sequence, taking the FFT of the processed sequence, and then postprocessing the results to give the desired transform. In this paper we show how a similar approach can be used for sequences which are known to have only odd harmonics. The approach is shown to be essentially the dual of the known method for time symmetry. Computer programs are included for implementing the special procedures discussed in this paper.