A comb spectrum evaluation problem arises in the channel estimation of pilot symbol-assisted modulation (PSAM) systems and also in the (de)modulation of multichannel communication system based on orthogonal frequency division multiplexing (OFDM). In this letter, we decompose an -component comb spectrum evaluation with transform length into 1) a fast Fourier transform evaluation of transform length of a length vector, 2) which in turn is obtained from the length input vector (by folding and scaling). This decomposition allows for the application of split-radix and radix-4 algorithms for evaluation of length transform and efficient computation of the length vector from the length input vector, which is classically termed as "pruning." When = 2 , the comb spectrum computation requires only 8 + 3 log 2 nontrivial complex multiplications, if 8. In addition, conditions under which comb spectrum evaluation can be done in ( log ) complex multiplies are identified.Index Terms-Comb spectrum, discrete Fourier transform (DFT), fast Fourier transform (FFT).
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