Fixed-point error analysis of Winograd basic DFT algorithms considering correlation between noise sources

Recently, Patterson and McClellan [1] have carried out the fixed-point error analysis of winograd Fourier transform algorithm assuming noise sources to be uncorrelated and have derived expressions for output NSR (noise to signal ratio). Such an assumption is not quite valid. A theoretically revised expression without making such an assumption has been obtained in case of Winograd short-length DFT algorithms. This involves the computation of correlation coefficients among noise sources. The revised results are verified by computer simulations and are found to be in close agreement with those predicted by Patterson and McClellan. It is, in general, observed that the basic modules introduce errors higher than those of FFT and require maximum of half a bit to maintain the same degree of precision.