Analysis of floating point roundoff errors in the estimation of higher-order statistics
A floating point roundoff error analysis in the estimation of higher-order statistics, moments or cumulants of real stationary processes from single data records is provided. Closed form expressions or upper bounds are derived for the mean and variance of the quantisation noise introduced in the estimation of the all-zero and all-T (diagonal slice) moments, power, skewness and kurtosis. Numerical and simulation results show that the roundoff noise can significantly affect the moment and cumulant estimates, especially when long data records are employed for the purpose of reducing the estimation variance. The obtained results can provide guidelines in choosing a processor with the appropriate register length (in number of bits) in applications that require the calculation of higher-order statistics.
- C.L. Nikias , M.R. Ranguveer . Bispectrum estimation: A digital signal processing framework. Proc. IEEE , 7
- J.M. Mendel . Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications. Proc. IEEE , 3 , 278 - 305
- M. Rosenblatt . (1985) , Stationary sequences and random fields.
- S. Bellini , F. Rocca , E. Biglieri , G. Prati . (1986) Blind deconvolution: Polyspectra or bussgang techniques, Digital communications.
- A.G. Bessios , C.L. Nikias . FFT based bispectrum computation on polar rasters. IEEE Trans. , 1 , 2535 - 2539
- Stellakis, H., Manolakos, E.: `An integrated architecture for the real time estimation of higher-order cumulants', Proceedings of ICASSP '93, 1993, Minneapolis, MN, USA, p. IV220–IV223.
- A.V. Oppenheim , R.W. Schafer . (1975) , Digital signal processing.
- R.D. Gitlin , J.E. Mazo , M.G. Taylor . On the design of gradient algorithms for digitally implemented adaptive filters. IEEE Trans. , 2
- C. Caraiscos , B. Liu . A roundoff error analysis of the LMS adaptive algorithm. IEEE Trans. , 1 , 34 - 41
- B. Zeng , Y. Neuvo . Analysis of floating point roundoff errors using dummy multiplier coefficient sensitivities. IEEE Trans. , 6 , 590 - 601
- A. Papoulis . (1991) , Probability, random variables, and stochastic processes.
- Tsouras, N.: `Development of floating point arithmetic software for evaluation of signal processing applications', 1990, BASc thesis, University of Toronto.