This correspondence presents some results in fixed-point error analysis of fast Fourier transform algorithms. Two kinds of schemes for preventing overflow are considered in the analysis. The results, obtained for the decimation-in-frequency form of the algorithm, are compared with those of decimation-in-time. The results show that the error performance of the decimation-in-frequency algorithm is better than that of decimation-in-time.

An expression for the output noise-to-signal ratio is derived, taking into account the correlation between the truncation errors, when fast Fourier transform is computed in fixed-point arithmetic. A few assumptions, made in the analysis, are verified by computer simulations. The output noise-to-signal ratios predicted by the new expression and the old expression (which is derived under the assumption that the truncation errors are uncorrelated) are compared with the experimental results. It is shown that the predicted values based on the new results fall short of the experimental results by atmost 22%, while those predicted by the old results fall short by as much as 135.7%.