Distribution of the Filtered Output of a Quadratic Rectifier Computed by Numerical Contour Integration

IEEE Transactions on Information Theory

Volumn 32, Issue 4, 1986, Pages 450-463

  Helstrom, Carl W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - INTEGRATION; PROBABILITY - RANDOM PROCESSES; SPECTRUM ANALYSIS;

LAPLACE INVERSION INTEGRAL; MEAN-ZERO GAUSSIAN PROCESS POWER; NUMERICAL CONTOUR INTEGRATION; PROBABILITY DISTRIBUTION; QUADRATIC RECTIFIER OUTPUT;

SIGNAL FILTERING AND PREDICTION;

EID: 0022751932     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1986.1057204     Document Type: Article

References (24)

1. M. Kac and A. J. F. Siegert, “On the Theory of noise in radio receivers with square law detectors,” J. Appl. Phys., vol. 18, pp. 383–397, Apr. 1947.
2. D. Slepian, “Fluctuations of random noise power,” Bell Syst. Tech. J., vol. 37, pp. 163–184, Jan. 1958.
3. U. Grenander, H. O. Poliak, and D. Slepian, “The distribution of quadratic forms in normal variates: A small sample theory with applications to spectral analysis,” J. Soc. Ind. Appl. Math., vol. 7, pp. 374–401, 1959.
4. W. Freiberger and U. Grenander, “Approximate distributions of noise power measurements,” Q. Appl. Math., vol. 17, pp. 271–283, 1959.
5. M. I. Schwartz, “Distribution of the time-average power of a Gaussian process,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 17–26, Jan. 1970.
6. S. Y. Kwon and M. M. Shehadeh, “ Output statistics of an integrating square-law device with band-limited Gaussian input,” Int. J. Electron., vol. 41, pp. 333–346, 1976.
7. D. R. Hummels, C. Adams, and B. K. Harms, “Filter selection for receivers using square-law detection,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-19, pp. 871–883, Nov. 1983.
8. C. W. Helstrom, “Evaluating the detectability of Gaussian stochastic signals by steepest descent integration,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-19, pp. 428–437, May 1983.
9. C. W. Helstrom and J. A. Ritcey, “Evaluating radar detection probabilities by steepest descent integration,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-20, pp. 624–633, Sept. 1984.
10. C. W. Helstrom, “Computation of photoelectron counting distributions by numerical contour integration,” J. Opt. Soc. Amer. A, vol. 2, pp. 674–682, May 1985.
11. G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable. New York: McGraw-Hill, 1966, pp. 257ff.
12. H. A. Spang, III, “A review of minimization techniques for nonlinear functions,” SIAM Rev., vol. 4, pp. 343–365, 1962.
13. C. Schwartz, “Numerical integration of analytic functions,” J. Comput. Phys., vol. 4, pp. 19–29, 1969.
14. S. O. Rice, “Efficient evaluation of integrals of analytic functions by the trapezoidal rule,” Bell Syst. Tech. J., vol. 52, pp. 707–722, May-June 1973.
15. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, NBS Appl. Math. Series, no. 55, U.S. Gov't Printing Office, 1964.
16. S. O. Rice, “Uniform asymptotic expansions for saddle point integrals—Application to a probability distribution occurring in noise theory,” Bell Syst. Tech. J., vol. 47, pp. 1971–2013, Nov. 1968.
17. R. Lugannani and S. O. Rice, “Saddlepoint approximation for the distribution of the sum of independent random variables,” Adv. Appl. Probab., vol. 12, pp. 475–490, 1980.
18. C. W. Helstrom, “Approximate evaluation of detection probabilities in radar and optical communications,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-14, pp. 630–640, July 1978.
19. A. J. F. Siegert, “A systematic approach to a class of problems in the theory of noise and other random phenomena—Part II, Examples,” IRE Trans. Inform. Theory, vol. IT-3, pp. 38–43, Mar. 1957.
20. F. Schweppe, “Evaluation of likelihood functions for Gaussian signals,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 61–70, Jan. 1965.
21. D. Slepian and E. Sonnenblick, “Eigenvalues associated with prolate spheroidal wavefunctions of zero order,” Bell Syst. Tech. J., vol. 44, pp. 1745–1760, Oct. 1965.
22. H. L. Van Trees, Detection, Estimation, and Modulation Theory, vol. I, New York: Wiley, 1968, ch. 6, sec. 3, pp. 515–575.
23. R. E. Kalman and R. C. Bucy, “New results in linear filtering and prediction theory,” Trans. ASME, ser. D, vol. 83, pp. 95–107, 1961.
24. R. W. Hornbeck, Numerical Methods. New York: Quantum, 1975, pp. 194–196.