Limited dynamic range of spectrum analysis due to roundoff errors of the FFT

Roundoff errors of the block-float fast Fourier transform (FFT) are treated. Special emphasis is given to the case when signals containing sine waves are analyzed. In the detection and analysis of sine waves, root-mean-square values and overall signal-to-noise ratios do not provide adequate information. An analysis of the maximum values is suggested, and the achievable dynamic range is given. It is shown that in contrast to the common understanding, the dynamic range does not significantly depend on the point number of the FFT, when the roundoff errors originate dominantly from the arithmetic roundings within the FFT