Filter-bank interpretation and fixed-point numerical accuracy of subband FFT

The two main parts of the subband FFT presented recently [1],[2], a preprocessing Hadamard-transform stage and a 'correction' stage, are interpreted as a filter-bank-plus-recombination network. This interpretation is now studied in detail in terms of different filters' impulse responses in full-band and partial-band cases. The approach to a fix-point error analysis as known for, e.g., the radix-2 decimation-in-time Cooley-Tukey (CT-) FFT [3],[4] is applied to the SB-FFT. A comparison between the two FFT's is given for the full-band case. The effect of coefficient errors on the zero-pattern of the filter-bank is explained. A new measure for the coefficient error is introduced. According to this measure, the coefficient error in a channel k can be described by adding the linear distortion in this channel to the sum of the aliasing effects of all other channels on channel k. In a partial-band case, the approximation errors inherent in the SB-FFT combine with the coefficient error; this is described in a recursive form and explained by means of a numerical example for a simulated case.