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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 5 — May. 1, 1978
  • pp: 568–572

Investigations of errors in sample autocovariance functions and their corresponding power spectra

S. A. Armstrong and P. T. Gough  »View Author Affiliations


JOSA, Vol. 68, Issue 5, pp. 568-572 (1978)
http://dx.doi.org/10.1364/JOSA.68.000568


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Abstract

This paper concerns the calculation of autocovariance (autocorrelation) functions and the corresponding power spectra from a set of finite samples selected from the infinite population. In many optical experiments involving statistical fluctuations we wish to subtract the population mean from each measurement when the population mean is unknown. It is shown that subtracting the sample mean from each sample measurement leads to definite and predictable errors in the autocovariance function and its corresponding power spectrum. We show in a computer-generated example that the error introduced has significance in the autocovariance function but has much less significance in the power spectrum.

© 1978 Optical Society of America

Citation
S. A. Armstrong and P. T. Gough, "Investigations of errors in sample autocovariance functions and their corresponding power spectra," J. Opt. Soc. Am. 68, 568-572 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-5-568


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References

  1. J. C. Dainty and R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.
  2. S. A. Armstrong and B. J. Thompson, "Comparison of Coherent and Incoherent Spectral Analysis Techniques in Image Evaluation," in Data Extraction and Classification from Film (SPIE publication, 1977), Vol. 117.
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  5. P. Dobberstein, "Coupling Between Light and Surface Plasma- Waves Via Non-Gaussian Surface Roughness," Phys. Lett. A 31, 307 (1970).
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  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 21.
  8. Reference. 1, pp. 277–279.
  9. G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968), p. 179.
  10. E. L. O'Neill and A. Walther, "A problem in the determination of correlation functions," J. Opt. Soc. Am. 67, 1125 (1977).
  11. Ref. 9, pp. 179–180.
  12. W. Davenport and W. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), p. 69.
  13. Reference. 9, Sec. 6.3.4.
  14. E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 98.

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