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, &Dgr;fta, and a sampling frequency, fs, is chosen so that fs=N&Dgr;fta/S. S is a spacing given by S=Mw 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 &Dgr;fta=S&Dgr;f where &Dgr;f is a frequency bandwidth.