Detection and Extraction of Signals in Noise from the Point of View of Statistical Decision Theory. I

Previous article Next article Detection and Extraction of Signals in Noise from the Point of View of Statistical Decision Theory. IDavid Middleton and David Van MeterDavid Middleton and David Van Meterhttps://doi.org/10.1137/0103017PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1.1 Abraham Wald, Statistical Decision Functions, John Wiley J. Appl. Phys., 20 (1949), p. 334 CrossrefISIGoogle Scholar3.6 D. Van Meter, Masters Thesis, Optimum decision systems for the reception of signals in noise, Doctoral Dissertation, Harvard, 1955, Jan., pgs. (3–24) et seq. Google Scholar3.7 David Middleton, Information loss attending the decision operation in detection, J. Appl. Phys., 25 (1954), 127–128 MR0060799 (15,728i) ISIGoogle Scholar3.8 Abraham Wald, Sequential Analysis, John Wiley & Sons Inc., New York, 1947xii+212 MR0020764 (8,593h) Google Scholar3.9 A. Wald and , J. Wolfowitz, Optimum character of the sequential probability ratio test, Ann. Math. Statistics, 19 (1948), 326–339 MR0026779 (10,201e) CrossrefISIGoogle Scholar3.10 M. Schwartz, Masters Thesis, A statistical approach to the automatic search problem, Doctoral Dissertation, Harvard, 1951, June Google Scholar3.11 David Middleton, Statistical criteria for the detection of pulsed carriers in noise. I, J. Appl. Phys., 24 (1953), 371–378 10.1063/1.1721290 MR0055652 (14,1105c) CrossrefISIGoogle Scholar3.12 J. V. Harrington, An analysis of the detection of repeated signals in noise by binary integration, Lab. Tech. Report, 13, (Mass. Inst. Tech.), 1952, Aug. 14 Google Scholar3.13 I. S. Reed, Analysis of signal detection by sequential observer, Lincoln Lab. Tech. Report, 20, (Mass. Inst. Tech.), 1953, March 12 Google Scholar3.14 W. C. Fox, Signal detectability: A unified description of statistical methods employing fixed and sequential observation processes, Tech. Rept., 19, Electronic Defense Group, Univ. of Michigan, 1953, Dec., See also ref.1.34. Google Scholar3.15 H. Blasbalg, Theory of sequential filtering and its application to signal detection and classification, Rad. Lab. Tech.,Report, AF-8, The Johns Hopkins Univ., 1954, Oct. 18 Google Scholar3.16 J. Bussgang, Masters Thesis, Sequential detection of signals in noise, Doctoral Dissertation, Harvard, 1955, Jan. Google Scholar3.17 J. Bussgang and , D. Middleton, Sequential detection of signals in noise, Cruft Lab. Tech. Report, 115, Harvard Univ., 1955, March,(Also, An analysis of optimum sequential detectors, presented at I.R.E., Wescon meeting, San Francisco, August, 1955.) Google Scholar4.1 J. L. Hodges, Jr. and , E. L Lehmann, Some problems in minimax point estimation, Ann. Math. Statistics, 21 (1950), 182–197 MR0035949 (12,36g) CrossrefISIGoogle Scholar4.2 H. Cramér, Mathematical methods of statistics, Princeton, 1946 Google Scholar4.3 Ulf Grenander, Stochastic processes and statistical inference, Ark. Mat., 1 (1950), 195–277 MR0039202 (12,511f) CrossrefGoogle Scholar4.4 A. Wald, Contributions to the theory of statistical estimation and testing hypothesis, Ann. Math. Statistics, 21 (1950), 182–, Theorems 5 and 6. CrossrefISIGoogle Scholar4.5 E. J. G. Pitman, The estimation of location and scale parameters of a continuous population of any given form, Biometrika, 30 (1939), 391– CrossrefGoogle Scholar4.6 M. A. Girshick and , L. J. Savage, Bayes and minimax estimates for quadratic loss functions, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 53–73 MR0045365 (13,571h) Google Scholar4.7 R. C. Phidlips and , P. R. Weiss, Theoretical calculation on best smoothing of position data for gunnery prediction, Rad. Lab. Rept., 532, (Mass. Inst. Tech.), 1944 Google Scholar4.8 John von Neumann and , Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, N. J., 1947xviii+641 MR0021298 (9,50f) Google Scholar4.9 J. C. C. McKinsey, Introduction to the theory of games, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1952x+371 MR0050248 (14,300d) Google ScholarA.1 Kari Karhunen, Zur Spektraltheorie stochastischer Prozesse, Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys., 1946 (1946), 7– MR0023012 (9,292h) Google ScholarA.2 A. J. F. Siegert, Passage of Stationary Processes Through Linear and Non-Linear Devices, Trans. Inst. Radio Engrs., PGIT—3 (1954), 4– Google ScholarA.3 R. C. Davis, On the theory of prediction of non-stationary stochastic processes, J. Appl. Phys., 23 (1952), 1047–1053 10.1063/1.1702343 MR0050214 (14,295f) CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Hypothesis Testing of Gaussian Processes with Composite AlternativesJournal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 2 | 28 July 2006AbstractPDF (1413 KB)The Detection of Radar Echoes in Noise. IJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2 | 10 July 2006AbstractPDF (2758 KB) Volume 3, Issue 4| 1955Journal of the Society for Industrial and Applied Mathematics173-261 History Submitted:14 March 1955Published online:28 July 2006 InformationCopyright © 1955 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0103017Article page range:pp. 192-253ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics