Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T18:44:22.522Z Has data issue: false hasContentIssue false

The optimum processing of clipped signals: an approach based an a likelihood ratio statistic

Published online by Cambridge University Press:  17 February 2009

Annette Dobson
Affiliation:
Department of Mathematics, University of Newcastl, Newcastle, N. S. W. 2308.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The likelihood ratio approach to the detection of small signals in the presence of noise is investigated in the case where the available data have been clipped. The statistic obtained is the ratio of orthant probabilities and appears intractable; accordingly an approximation to this statistic is developed by truncating an appropriate Taylor expansion. Approximations are obtained for the mean and variance of this modified statistic and compared with those obtained from computer simulations.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Blachman, N. M., “The signal × signal, noise × noise, and signal × noise output of a nonlinearity”, IEEE Trans. Inform. Theory IT-14 (1968), 2127.CrossRefGoogle Scholar
[2]Edelblute, D. J., Fisk, J. M. and Kinnison, G. L., “Criteria for optimum signal detection for arrays”, J. Acoust. Soc. Amer. 41 (1967), 199205.CrossRefGoogle Scholar
[3]Ekre, H., “Polarity coincidence correlation detection of a weak noise source”, IEEE Trans. Inform. Theory IT-9 (1963), 1823.CrossRefGoogle Scholar
[4]Faran, J. J. and Hills, R. Jr, “The application of correlation techniques to acoustic receiving systems”, Technical Memo No. 28, Acout. Res. Lab., Harvard, (1952).CrossRefGoogle Scholar
[5]Franks, L. E., Signal theory (Prentice-Hall, Englewood Cliffs, N. J., 1969).Google Scholar
[6]Frost, W., “A likelihood ratio statistic for the detection of signals using clipped data”, M. Math. Thesis, University of Newcastle (in preparation).Google Scholar
[7]Johnson, N. L. and Kotz, S., Distributions in statistics: continuous multivariate distributions (John Wiley, New York, 1972).Google Scholar
[8]Kanefsky, M., “Detection of weak signals with polarity coincidence arrays”, IEEE Trans. Inform. Theory IT-12 (1966), 260268.CrossRefGoogle Scholar
[9]Keats, R. G. and Cooper, J., “The optimum processing of clipped signals; an approach based on minimum signal distortion”, J. Austral. Math. Soc. Ser. B 22 (1980), 175184.CrossRefGoogle Scholar
[10]Keats, R. G. and Yu, V. K-K., “A generalisation of the study of sum and square law signal processors with multiple clipped inputs”, J. Austral. Math. Soc. Ser. B 19 (1976), 294315.CrossRefGoogle Scholar
[11]Marsaglia, G. and Bray, T. A., “A convenient method for generating normal variables”, SIAM Rev. 6 (1964), 260264.CrossRefGoogle Scholar
[12]Plackett, R. L., “A reduction formula for normal multivariate integrals”, Biomegrika 41 (1954), 351360.CrossRefGoogle Scholar
[13]Schuitheiss, P. M. and Tuteur, F. B., “Optimum and sub-optimum detection of Gaussian signals in an isotropic Gaussian noise field, Part II: degradation of detectability due to clipping”, IEEE Trans.an Military Electronics MIL-9 (1965) 208211CrossRefGoogle Scholar
[14]Thomas, J. B. and Williams, T. R., “On the detection of signals in nonstationary noise by product arrays”, J. Acoust. Soc. Amer. 31 (1959), 453462.CrossRefGoogle Scholar
[15]Usher, T. Jr, “Signal detection by arrays in noise fields with local variations”, J. Acoust. Soc. Amer. 36 (1964), 14441449.CrossRefGoogle Scholar
[16]Wald, A., Sequential analysis (John Wiley, New York, 1947).Google Scholar