Error propagation in fourier transforms

René Alt

Mathematics and Computers in Simulation (MATCOM), 1978, vol. 20, issue 1, 37-43

Abstract: The Fourier transform has long been of great use in simulating mathematical or physical phenomena, especially in signal theory. However the finite length representation of numbers introduces round-off errors in computing. Here, developing a new point of view on the topic, we give an evaluation of the total relative mean square error in the computation of direct and fast Fourier transforms using floating point artihmetic. Thus we show that in direct Fourier transforms the output noise-to-signal ratio is equivalent to N or N2 according to whether the arithmetic is a rounding or a chopping one, whereas for fast Fourier transforms it is equivalent to log2(N) or [log2(N)]2, with N being the number of points of the signal. Good agreement with numerical results is observed.

Date: 1978
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378475478900526
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:20:y:1978:i:1:p:37-43

DOI: 10.1016/0378-4754(78)90052-6

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().