An accurate error analysis model for fast Fourier transform

Author

Ma, Yutai

Author_Institution

Inst. of Comput. Technol., Acad. Sinica, Beijing, China

Volume

45

Issue

6

fYear

1997

fDate

6/1/1997 12:00:00 AM

Firstpage

1641

Lastpage

1645

Abstract

An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm. With the model, an accurate error expression and error variance for the computation of FFT are derived. This correspondence deals with fixed-point and block floating-point arithmetic. Simulation results agree closely with the theoretical predicted ones. We find that some roundoff errors at different stages correlate with each other. The density of correlations is closely associated with the round-off approach used in butterfly calculations

Keywords

correlation theory; digital arithmetic; error analysis; fast Fourier transforms; floating point arithmetic; roundoff errors; signal processing; accurate error analysis model; block floating-point arithmetic; butterfly calculations; density of correlations; digital signal processing; error expression; error propagation model; error variance; fast Fourier transform; fixed-point arithmetic; image processing; in-place decimation-in-time version; radix-2 FFT algorithm; roundoff errors; simulation; Acoustic signal detection; Biomedical signal processing; Detectors; Error analysis; Fast Fourier transforms; Robustness; Signal detection; Signal processing algorithms; Time frequency analysis; Transient analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.600005

Filename

600005