Effect of correlation between transactions errors on fixed-point fast Fourier transform analysis

A revised expression, taking the effect of correlation between truncation errors, is obtained for the output noise-to-signal when the fast Fourier transform (FFT) is computed in fixed-point arithmetic. The results are given for the two common forms of the FFT algorithmn, decimation in-frequency and in-time. The analysis assumes sign-magnitude (or 1´s complement) arithmetic and is presented in detail for the decimation-in-frequency (DIF) case. The correlation coefficients are computed analytically. A few assumptions, made in the analysis, are verified by computer simulations. The average variance of the output noise, due to the truncation errors, predicted by the new model is approximately twice the corresponding value predicted by the old model (which assumes that the truncation errors are uncorrelated). The output noise-to-signal ratios predicted by the revised and old expressions are compared with experimental results. It is shown that the revised result predicts much closer to the experimental results than the old.