New results in fixed-point fast Fourier transform error analysis

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%.