In this paper the analysis of overall quantization loss for the Radix-4 and Radix-8 Fast Fourier Transform (FFT) algorithms is extended to the case where the twiddle factor word length is different from the register word length. Simulation results, that validate the theoretical analysis, are then presented. Index Terms-DFT (Discrete Fourier Transform), FFT (Fast Fourier Transform), DIT (Decimation in Time), DIF (Decimation in frequency), and Quantization error (QE).

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The efficient computation of Discrete Fourier Transform (DFT) is an important issue as it is used in almost all fields of engineering for signal processing. This paper presents a different form of Radix-2 Fast Fourier Transform (FFT) based on Decimation in time (DIT) to compute DFT, discuss their implementation issues and derive it's signal to quantization noise ratio(SQNR) that further decreases the number of multiplication counts without affecting the number of additions of Radix-2 discrete Fourier Transform. It is achieved by simple scaling of Twiddle factor (TF) using a special scaling factor. This modification not only decreases the 2total flop counts from 5Nlog 2 N to '" 4 -Nlog2N (6.66% 3 fewer than the standard Radix-2 FFT algorithm) but also improves SQNR from � to 9 -2 b (l.6dB more than 2N2 15N2the standard Radix-2 FFT algorithm).

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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).