Fixed-point fast Fourier transform error analysis
Tran-Thong, Bede Liu · IEEE Transactions on Acoustics Speech and Signal Processing · 1976
A statistical model for roundoff errors is used to predict the output noise of the two common forms of the fast Fourier transform (FFT) algorithm, the decimations in-time and in-frequency. This paper deals with two's complement arithmetic with either rounding or chopping. The total mean-square errors and the mean-square errors for the individual points are derived for radix-2 FFT's. Results for mixed-radix FFT are also given.