Error analysis of Good-Winograd algorithm assuming correlated truncation errors

This paper investigates the error performance of the Good-Winograd algorithm (GWA) when implemented in fixed-point mode using sign magnitude or 1's complement arithmetic. Unlike the previous analysis, the present study assumes the noise sources (particularly the truncation errors due to complex scaling) to be correlated both inside and between stages. Expressions for output noise-to-signal ratio (NSR), taking the effect of the correlation between truncation errors in the same path of signal flow, are derived for minimum error ordering of the basic modules. The error predicted by the correlated model (present investigation) is approximately 170 percent of the corresponding value predicted by the uncorrelated model of Patterson and McClellan. On comparison of the results of both the models with the experimental findings, it is, in general, observed that the correlated model predicts results much closer to the corresponding experimental value. Furthermore, the GWA introduces errors almost identical to the correlated model of decimation-in-time (DIT) FFT and hence, with an equal number of data bits can maintain a similar degree of accuracy.