{"title":"The theory of signal detectability","authors":"W. W. Peterson, T. Birdsall, W. C. Fox","doi":"10.1109/TIT.1954.1057460","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057460","url":null,"abstract":"The problem of signal detectability treated in this paper is the following: Suppose an observer is given a voltage varying with time during a prescribed observation interval and is asked to decide whether its source is noise or is signal plus noise. What method should the observer use to make this decision, and what receiver is a realization of that method? After giving a discussion of theoretical aspects of this problem, the paper presents specific derivations of the optimum receiver for a number of cases of practical interest. The receiver whose output is the value of the likelihood ratio of the input voltage over the observation interval is the answer to the second question no matter which of the various optimum methods current in the literature is employed including the Neyman - Pearson observer, Siegert's ideal observer, and Woodward and Davies' \"observer.\" An optimum observer required to give a yes or no answer simply chooses an operating level and concludes that the receiver input arose from signal plus noise only when this level is exceeded by the output of his likelihood ratio receiver. Associated with each such operating level are conditional probabilities that the answer is a false alarm and the conditional probability of detection. Graphs of these quantities called receiver operating characteristic, or ROC, curves are convenient for evaluating a receiver. If the detection problem is changed by varying, for example, the signal power, then a family of ROC curves is generated. Such things as betting curves can easily be obtained from such a family. The operating level to be used in a particular situation must be chosen by the observer. His choice will depend on such factors as the permissable false alarm rate, a priori probabilities, and relative importance of errors. With these theoretical aspects serving as an introduction, attention is devoted to the derivation of explicit formulas for likelihood ratio, and for probability of detection and probability of false alarm, for a number of particular cases. Stationary, band-limited, white Gaussian noise is assumed. The seven special cases which are presented were chosen from the simplest problems in signal detection which closely represent practical situations. Two of the cases form a basis for the best available approximation to the important problem of finding probability of detection when the starting time of the signal, signal frequency, or both, are unknown. Furthermore, in these two cases uncertainty in the signal can be varied, and a quantitative relationship between uncertainty and ability to detect signals is presented for these two rather general cases. The variety of examples presented should serve to suggest methods for attacking other simple signal detection problems and to give insight into problems too complicated to allow a direct solution.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"97 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128569452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The detection of signals perturbed by scatter and noise","authors":"R. Price","doi":"10.1109/TIT.1954.1057473","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057473","url":null,"abstract":"In recent years, much study has been devoted to the problem of conveying information efficiently through channels in which the mess*-bearing waveforms may undergo distortion. Statistical methods have proven an effective tool with which to anslyze and synthesize transmission systems as a whole, especially where channel perturbations are of a.random nature. The statistical approach is particularly rewarding whan questions of receiver optimization are considered. Provided that the transmitter ePld channel conform to the realistic, yet very general, mdel proposed by Shannon,1 the ideal receiver assumes the form of a probability-computer. This result was recognized by Woodward and Davies,* and Van Vleck and M.dcUeton3 have similarly treated ideal detection as the testing of statistical hypotheses.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"37 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120896350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Binary coding","authors":"M. Golay","doi":"10.1109/TIT.1954.1057463","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057463","url":null,"abstract":"","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129373470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Information, organization and systems","authors":"J. Rothstein","doi":"10.1109/TIT.1954.1057475","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057475","url":null,"abstract":"The object of this paper is to develop and apply a mathematical concept of organization and of systems. It is very closely related to the information concept and provides the link whereby the theorems of communication theory become generalized and applicable to systems in general. Brief applications are given to system reliability, the significa.nce of organization theory for circuit design, and production and quality control for a systems viewpoint.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130191461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simulation of self-organizing systems by digital computer","authors":"B. G. Farley, W. A. Clark","doi":"10.1109/TIT.1954.1057468","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057468","url":null,"abstract":"A general discussion of ideas and definitions relating to self-organizing systems and their synthesis is given, together with remarks concerning their simulation by digital computer. Synthesis and simulation of an actual system is then described. This system, initially randomly organized within wide limits, organizes itself to perform a simple prescribed task.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127306347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An information-theoretical model of organizations","authors":"M. Kochen","doi":"10.1109/TIT.1954.1057467","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057467","url":null,"abstract":"","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126404233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A class of multiple-error-correcting codes and the decoding scheme","authors":"I. Reed","doi":"10.1109/TIT.1954.1057465","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057465","url":null,"abstract":"linear error-correcting codes used in communications. (14) I. S. Reed, “A class of multiple-errorcorrecting codes and the decoding scheme,” IRE. Trans. A class of multiple-error-correcting codes and the decoding scheme. more. less. I. Reed · Details · Authors · Fields of science · Bibliography · Quotations · Similar. linear error correcting codes used in communications (2).For bit study is to device a coding scheme which is able to detect and correct such errors (6). (8) Reed, I. S., 'Class of multiple error correcting codes and their decoding scheme'.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122260966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A study of ergodicity and redundancy based on intersymbol correlation of finite range","authors":"Satosi Watanabe","doi":"10.1109/TIT.1954.1057474","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057474","url":null,"abstract":"Some of the basic concepts of information theory are critically reviewed in the light of a generalized formulation of the theory of Markoff's chains, in which the initial and final states are sequences of symbols of different lengths, and occurrence of symbols is governed by inter-symbol correlation probability of finite range. In particular, the conditions of ergodicity and the structure of \"ergodic subsets\" of sequences of arbitrary length are carefully discussed. A mathematical method is developed to determine the \"range\" and \"strength\" of inter-symbol correlation. A brief summary of the content is given at the end of Section 1.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"577 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126892129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The human use of information-I: Signal detection for the case of the signal known exactly","authors":"W. P. Tanner, J. Swets","doi":"10.1109/TIT.1954.1057461","DOIUrl":"https://doi.org/10.1109/TIT.1954.1057461","url":null,"abstract":"A theory of visual detection is developed, based on the model provided by the theory of signal detectability,2 and, more generally, by the theory of statistical decision. Two experiments are reported which test some predictions of the theory for the case of the signal-known-exactly. These experiments demonstrate that the human observer tends toward optimum behavior, where optimum behavior is defined as that behavior which maximizes the expected gain from the decision. Their results show the proportion of correct detections to be dependent upon the proportion of false alarms; they indicate that neural activity is a power function of signal intensity. The data also demand a re-evaluation of the threshhold concept. Predictions are made for the data obtained using two different methods of response, forced-choice end yes-no, and the internal consistency of the theory is demonstrated. The predictions of the theory are compared with contrasting predictions of conventional sensory theory; the data are also related to conventional theory.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128462379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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