Error analysis and comparison of FFT implementation structures

A statistical model for roundoff errors is used to predict the output noise of most common forms of the fast Fourier transform (FFT) algorithm, the radix-2 and radix-4, with both decimation-in-time (DIT) and decimation-in-frequency (DIF). Two´s complement fixed-point data representation with either truncation, rounding, or convergent rounding is treated. The mean values and the variances of the error for the individual frequency points are derived from three radix-2-DIT butterflies, which differ in type and location of quantizations and are normally used in most integrated signal processors. Results for fixed-point and block floating-point FFTs are presented and compared with other approaches to error reduction that yield maximal speed and accuracy in a given architecture