METHOD AND APPARATUS TO REDUCE THE COMLEXITY OF THE CALCULATION OF THE FAST FOURIER TRANSFORM OF A SIGNAL CONTAINING TONES

摘要

Various methods and apparatuses are provided for performing a radix-M FFT (Fast Fourier Transform) upon N time domain samples to produce N/S frequency domain samples for detecting tones of dithers impressed on channels of a WDM (wavelength Division Multiplexed) optical signal. Successive tones have a tone frequency spacing, Deltafta, and a sampling frequency, fs, is chosen so that fs = NDeltafta/S. S is a spacing given by S = M<w> with w being an integer. The radix-M FFT is performed in k = logM(N) stages and within the stages a reduced number of radix-M computations, when compared to the number of radix-M computations of a conventional radix-M FFT, are performed on data points associated with the N time domain samples. This is possible because successive frequency domain samples of the N/S frequency domain samples differ by Deltafta = SDeltaf where Deltaf is a frequency bandwidth.