Propagation of measurement errors through the DFT

The objective of this research was to determine how magnitude and/or phase errors on frequency domain signal components affect the temporal signal components. The Lindeberg form of the central limit theorem was utilized to prove that the temporal signal components are asymptotically normal with known mean and variance. Further, these results are extended to show that the temporal signals are approximately normal with a known mean and variance, if the signal length N is large enough. Simulation results are included which confirm the theoretical results