Propagation of uncertainty in a discrete Fourier transform algorithm

The problem of evaluating the uncertainty that characterises discrete Fourier transform output data is dealt with, using a method based on a 'white box' theoretical approach. The main sources of uncertainty (quantization, time jitter, microprocessor finite wordlength) are analysed obtaining equations useful to evaluate the uncertainty in both module and phase output values, for any hardware configuration and for any algorithm operating condition. The theoretical results, 'verified by both simulation and experimental tests, can be particularly useful for any designer and user of DFT-based instruments, since they allow the measurement configuration to be optimised with respect to the final uncertainty. (C) 2000 Elsevier Science Ltd. All rights reserved.