Roundoff errors in fixed-point FFT

The general assumptions made about roundoff noise are that its samples form a white sequence. and they are uniformly distributed between plusmnq/2, where q is the size of the LSB. While this is often true, strange cases may appear, e.g. misleading peaks can occur in the spectrum. This paper investigates the roundoff error of fixed-point FFT. It reproduces the results of Welch (1969) with modern tools, points at an error in his simulations, and investigates the consequences of the violation of the assumption for almost pure sine waves. The maximum amplitude of spurious peaks is determined and the reduced dynamic range is given.