{"title":"Passage of stationary processes through linear and non-linear devices","authors":"A. Siegert","doi":"10.1109/IREPGIT.1954.6373397","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373397","url":null,"abstract":"Many problems in the theory of noise and other random functions can be formulated as the problem of finding the probability distribution of the functional $u = intlimits^infty_0 K(t') , V, (X (t'))dt'$ where K(t) and V(x) are known functions and x(t) is a random function of known statistical properties. The problem of finding the probability distribution of the noise output of a receiver consisting of a filter, a detector, and a second filter is of this type. Methods will be discussed which have led to solutions of this problem in some special cases. In the case of multidimensionally Markoffian x(t) the problem will be shown to be equivalent to an integral equation, which in many cases of interest reduces to a differential equation.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126363092","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":"Simpie games of strategy occurring in communication through natural languages","authors":"B. Mandelbrot","doi":"10.1109/IREPGIT.1954.6373405","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373405","url":null,"abstract":"The purpose of the investigation to be reported here differs in one essential respect from the purpose of most statistical studies on problems of communication. We wish to state this difference from the beginning, in order to avoid misunderstanding of the methods used later on. Most communication problems are, broadly speaking, engineering problems; that is, they deal with the construction and evaluation of new methods of communication, using one's knowledge of \"Nature,\" acquired elsewhere. Our problem is, broadly speaking, physical; we seek to improve our knowledge, or at least our description, of \"Nature\" by using models in which some statistical concepts, developed in the study of recent communication problems, are used side by side with such concepts of physics as were already used to solve older engineering problems. This difference of purpose will also explain an unessential character of this paper: the calculations are much simpler than in other papers of the symposium, because here one could choose the problems leading to simple theories by the present methods (but not by previous ones), whereas in other papers the problems were imposed.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"17 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126337277","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":"Detection of modulated noise-like signals","authors":"R. Deutsch","doi":"10.1109/IREPGIT.1954.6373403","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373403","url":null,"abstract":"The detection of several interfering modulated noise-like signals is described and an expression is derived for the resultant correlation function, The correlation function is used to demonstrate the modulation suppression action of a linear detector for the general case of signals of noise-like character. Since the detection process suppresses the temporal variations of the weaker signals in one portion of the output spectrum and the stronger signals in another, it is possible, under certain conditions, to effectively separate the modulation information of the original signals.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127092726","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":"Statistical theory of signal detection","authors":"D. Middleton","doi":"10.1109/IREPGIT.1954.6373398","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373398","url":null,"abstract":"A complete theory of detection is presented, which is capable of treating general types of signals (e.g. periodic, aperiodic, random) in noise of arbitrary statistical character. By proper formulation of the detection problem as a test of statistical hypotheses, the precise structure of the optimum detector can be specified and minimum detectable signals uniquely determined. For threshold reception (the problem of main interest) two classes of operation arise: if detection is coherent, as far as dependence on the input signal-to-noise ratio is concerned one has a linear system, no matter how weak the signal; on the other hand for incoherent reception one always has a quadratic dependence on this input ratio (modulation suppression). Threshold reception in these two instances requires respectively a suitably weighted cross-correlation of the received data with the a priori known signal, or a suitably weighted autocorrelation of the received data with itself. The optimum detector is in general a computer, involving non-linear operations and terminating in a decision operation, which depends on the type of statistical test (e.g. Neyman-Pearson, Ideal, Sequential, etc.) defining the observer. The threshold of decision is necessarily determined by a suitable betting or cost curve. (Both discrete (digital) and continuous (analog) sampling of the data are considered.) In this way optimum performance, consistent with the external constraints, is specified, and the extent by which actual systems depart from this limiting optimum can be calculated.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129320050","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":"Mlnimum-cost encoding of information","authors":"N. Blachman","doi":"10.1109/IREPGIT.1954.6373407","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373407","url":null,"abstract":"Haying determined a cost in energy, time, or money of transmitting each of a set of symbols (e.g., dot and dash, pulses of various amplitudes, etc.), one may inquire as to the nature of a code using these symbols which will transmit a given amount of information at the least cost, or will transmit information at a given rate for the least cost per unit time. Such a code must use each symbol with a relative frequency given by a negative exponential of a linear combination of its cost and duration in the case of a noiseless communication channel. If noise is present, the cost of each symbol is effectively increased by a multiple of its \"prevarication,\" i.e., the entropy of the received symbol when only the given symbol is transmitted.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132077631","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 response of linear systems to non-Gaussian noise","authors":"B. Gold, G. Young","doi":"10.1109/IREPGIT.1954.6373400","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373400","url":null,"abstract":"A fairly broad class of problems deals with the way certain properties of noise are altered on passage through a linear system. Fig. l defines these properties. If any n instants of time are chosen and if boundary value problems of the zero crossing type are omitted, the specification of the n dimensional probability distribution yields the most complete statistical information. Very often, however, this information is difficult or impossible to find and it is useful to obtain properties (2) and (3) of Fig. 1 without actually knowing property (1). Briefly, an nth order random process is defined by no more than an n dimensional probability distribution. Given a higher order distribution, it can be reduced to order n. The example in Fig. 1 shows how, for a 2nd degree (a Markoff) process, a trivariate form can be expressed in terms of bivariate and lower forms. A stationary process is one whose statistical properties do not depend on the choice of time reference.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129722087","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":"Generalized servomechanism evaluation","authors":"W. P. Caywood, R. C. Lyman, W. Kaufman","doi":"10.1109/IREPGIT.1954.6373408","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373408","url":null,"abstract":"In the course of staking general evaluations of servo systems utilizing magnetic amplifiers, the inadequacy of classical methods becomes immediately evident. Statistical treatment of the signal and the system error is neccessary criteria of performance other than the quadratic are essential; and it is possible that accurate evaluation can result only from including the effects of the inherent non-linearities of the system. Progress to date has resulted in three separate approaches to the problem: a) A computer which includes a system analog, and an error criterion and integrating circuit, and which accepts statistically typical signals from a signal storage or generating device. There results a single number describing the performance of the system. b) An analytical method applicable only to linear systems, which makes use of the atrtocorrelation function of the signal and noise inputs, and also of the higher moment correlation fkutions of the two. c) An analytical method applicable in instanrces when the signal spectrum changesabruptly. The anaysis is applicable only to linear systems and considers a quadratic criterion.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117170397","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 use of the method of maximum likelihood in estimating continuous-modulated intelligence which has been corrupted by noise","authors":"D. Youla","doi":"10.1109/IREPGIT.1954.6373402","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373402","url":null,"abstract":"A signal is received in the time interval (t ? T ? ? ? t). It is known that this signal is composed of noise plus intelligence a(t) which is statistical in nature and which has been modulated in some known way. Assuming that both intelligence and noise are Gaussian (although not necessarily stationary) time series, the analog of the classical maximum-likelihood estimate for ?(t) is derived. The advantage of this approach is that it can handle arbitrary types of modulation. For unmodulated stationary intelligence and stationary noise, the solution reduces to that of Zadeh and Ragazzini. In the general case, the optimum estimate is given as the solution of a pair of integral equations. The amplitude-modulated case is treated in some detail. The application of the maximum-likelihood technique to problems involving arbitrary modulation was first suggested, as far as the author is aware, by F. W. Lehan and R. J. Parks of the Jet Propulsion Laboratory.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115767248","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":"Optimum pulse-time determination","authors":"A. Mallinckrodt, T. Sollenberger","doi":"10.1109/IREPGIT.1954.6373409","DOIUrl":"https://doi.org/10.1109/IREPGIT.1954.6373409","url":null,"abstract":"A common problem in radar, navigation systems or pulse-time modulation systems is that of determination of the delay or time of arrival of a pulse or other distinctive modulation form. while considerable effort has been directed toward the optimization in various senses of the signal-to-noise ratios for such signals, the problem of the most accurate determination of time delay of signals in noise bas, with a few noteworthy exceptions, been taken for granted. It is of interest to examine this problem for its own sake, not only as indicative of optimum circuit practice, but, more important, in order to make clear the fundamental accuracy limitations and the manner in which these limitations depend upon signal and noise parameters. The consideration of this paper is limited to the case where there is no doubt as to the existence nor approximate position of a pulse but where the accuracy of determination of pulse position is limited by noise. This case is therefore more representative of the problems of high accuracy systems such as Loran or shoran than of radar.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1954-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131616483","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":"Discussion on Dr. Mackay's paper on 'Quantum Aspects of Scientific Information'","authors":"D. Mackay","doi":"10.1109/TIT.1953.1188583","DOIUrl":"https://doi.org/10.1109/TIT.1953.1188583","url":null,"abstract":"Could Mr. MacKay clarify the trend of his paaper in its relation to the preceding paper by Dr. Gabor, and to Lord Cherr!ell's work, referred to by a previous speaker, on the interpretation of quantum theory? Whereas Dr. Gabor had started from quantum theory and deduced the ultimate 'bits' of communication theory from it, Mr. MacKay seemed to be starting from the other end, and attempting to deduce quanta from logical analysis into atomic propositions. Mr. MacKay would perhaps agree that this logical approach at beat left an undetermined constant which could only be obtained by experiment.","PeriodicalId":134468,"journal":{"name":"Trans. IRE Prof. Group Inf. Theory","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1953-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122364301","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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