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Information Theory, IRE Transactions on

Issue 2 • Date April 1961

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Displaying Results 1 - 11 of 11
  • Effect of hard limiting on the probabilities of incorrect dismissal and false alarm at the output of an envelope detector

    Publication Year: 1961 , Page(s): 60 - 66
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (989 KB)  

    This paper is concerned with the effect of hard limiting on the signal detectability of a system consisting of a limiter, narrow-band filter, and envelope detector in cascade. The input to the system is a pulsed IF signal immersed in noise whose power spectrum is uniform over a band of width W cycles. Assuming that the noise bandwidth W is much larger than the bandwidth of the narrow-band filter, the probability distribution of the output of the filter will approach Gaussian. A bivariate Edgeworth series approximation is necessary to handle the narrow-band-filter output since the "in-phase" and "quadrature" components of the narrow-band-filter output are statistically dependent random variables. An expression is derived for the probability of incorrect dismissal that requires the numerical evaluation of single integrals only. From the same bivariate Edgeworth series, an expression is derived for the probability-density function of the output of the envelope detector for the zero-input-signal case. Subsequent integration leads to the probability of false alarm. View full abstract»

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  • On the asmptotic efficiency of locally optimum detectors

    Publication Year: 1961 , Page(s): 67 - 71
    Cited by:  Papers (59)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (761 KB)  

    A detector examines an unknown waveform to determine whether it is a mixture of signal and noise, or noise alone. The Neyman-Pearson detector is optimum in the sense that for given false alarm probability, signal-to-noise ratio, and number of observations, it minimizes the false dismissal probability. This detector is optimum for all values of the signal-to-noise ratio, and its implementation is usually quite complicated. In many situations it is desired to detect signals which are very weak compared to the noise. The locally optimum detector is defined as one which has optimum properties only for small signal-to-noise ratios. It is proposed as an alternative to the Neyman-Pearson detector, since in practice it is usually only necessary to have a near-optimum detector for weak signals, since strong signals will be detected with reasonable accuracy even if the detector is well below optimum. In order to evaluate the performance of the locally optimum detector, it is compared to the Neyman-Pearson detector. This comparison is based on the concept of asymptotic relative efficiency introduced by Pitman for comparing hypothesis testing procedures. On the basis of this comparison, it is shown that the locally optimum detector is asymptotically as efficient as the Neyman-Pearson detector. A number of applications to several detection problems are considered. It is found that the implementation of the locally optimum detector is less, or at most as complicated as that of the Neyman-Pearson detector. View full abstract»

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  • Frequency differences between two partially correlated noise channels

    Publication Year: 1961 , Page(s): 72 - 81
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1341 KB)  

    Approximate probability distributions of the difference frequency between two noise channels which contain dissimilar Gaussian, rectangular or triple-tuned RLC band-pass filters are calculated. For noise channels that differ only in time delay, a proportionality between rate of change of instantaneous frequency and the difference frequency is assumed. For dissimilar filters, an approximately equivalent single filter-time delay process is defined. The single filter is determined from the moment averages of the two dissimilar filters, while the equivalent time delay is computed by equating the magnitude of the correlation function in the two processes. View full abstract»

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  • Complementary series

    Publication Year: 1961 , Page(s): 82 - 87
    Cited by:  Papers (407)  |  Patents (68)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (882 KB)  

    A set of complementary series is defined as a pair of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any one given separation in one series is equal to the number of pairs of unlike elements with the same given separation in the other series. (For instance the two series, 1001010001 and 1000000110 have, respectively, three pairs of like and three pairs of unlike adjacent elements, four pairs of like and four pairs of unlike alternate elements, and so forth for all possible separations.) These series, which were originally conceived in connection with the optical problem of multislit spectrometry, also have possible applications in communication engineering, for when the two kinds of elements of these series are taken to be +1 and -1, it follows immediately from their definition that the sum of their two respective autocorrelation series is zero everywhere, except for the center term. Several propositions relative to these series, to their permissible number of elements, and to their synthesis are demonstrated. View full abstract»

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  • Signal detection by adaptive filters

    Publication Year: 1961 , Page(s): 87 - 98
    Cited by:  Papers (27)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1593 KB)  

    Communication engineers are now giving increased attention to detection systems which are able to adjust their own structure so as to be optimum for the particular detection problem of the moment. This paper describes a system which is capable of adapting and optimizing its response to the class of pulse signals whose individual pulses are less than T seconds in duration. The analysis and synthesis of the adaptive system is facilitated by the use of an orthogonal function decomposition of the received signal. The use of the orthogonal decomposition permits synthesis of optimum linear filters by various circuit techniques, several of which have been reported elsewhere. The structure of the system utilizing such a decomposition is described in detail. Since the operation of the adaptive filter is based upon signal detection and estimation in noise backgrounds, considerable attention is devoted to the relationship between optimum signal detection and estimation. The methods of statistical decision theory are used. A program to test the validity of the approximations and assess the over-all system performance was carried out by simulation of the system on both analog and digital computers. The results of these experimental runs are described. View full abstract»

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  • The coding of pictorial data

    Publication Year: 1961 , Page(s): 99 - 104
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (757 KB)  

    We are concerned with the problem of designing an efficient general method of coding two-level pictorial data. Both exact and approximate coding techniques are illustrated. A pilot experiment is presented, in which a digital computer was used to realize two-dimensional predictive coding. Although the resulting compression was not great, there are reasons for believing that this procedure would be more successful with realistic pictorial data. Further experiments, which made use of approximation methods are described. These methods arose from the application of pattern recognition theory to the present problem. Their use, either independently or prior to predictive coding, yielded compression significantly greater than that attained by predictive coding alone. View full abstract»

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  • On singular and nonsingular optimum (Bayes) tests for the detection of normal stochastic signals in normal noise

    Publication Year: 1961 , Page(s): 105 - 113
    Cited by:  Papers (5)
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    The necessary and sufficient ( n . and s .) conditions for the nonsingularity, i.e., regularity, and for the singularity of optimum tests for the presence of one Gaussian process vs another on a finite sample are established, for both nonstationary and stationary processes, including those with nonrational spectra. In the stationary cases, the condition may be expressed alternatively in terms of an integral of suitable spectral ratios when the random processes possess rational spectra and for certain classes of nonrational spectra as well. Equivalently, for rational spectra the n . and s . condition for nonsingularity is that the spectral ratio approach unity as frequency becomes infinite and that the spectral ratio be finite and nonzero for all frequencies, while for singularity the n . and s . condition requires that this ratio differ from unity in the limit or if unity in the limit, that this ratio vanish or be unbounded at some one (or more) finite frequencies. Some of the implications of these results in applications to signal detection are considered, and a method of solution of an associated class of integral equations, of the type begin{equation} int_{0-}^{T+} L(tau, u)K(bar u - t bar) du = G(t, tau), O - < t, tau < T+ end{equation} where K is a rational kernel and G is suitably specified, is briefly outlined. Specific results in the case of RC and LRC noise kernels, with G correspondingly the difference of two (different) RC or LRC covariance functions, are also given. View full abstract»

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  • A lower bound for error-detecting and error-correcting codes (Corresp.)

    Publication Year: 1961 , Page(s): 114 - 118
    Cited by:  Papers (1)
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  • A simple proof of an inequality of McMillan (Corresp.)

    Publication Year: 1961 , Page(s): 118
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (127 KB)  

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  • Note on an integral equation occurring in the prediction, detection, and analysis of multiple time series (Corresp.)

    Publication Year: 1961 , Page(s): 118 - 120
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (382 KB)  

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  • Review of 'Testing Statistical Hypotheses' (Lehmann, E. L.; 1959)

    Publication Year: 1961 , Page(s): 125
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    Freely Available from IEEE

Aims & Scope

This Transactions ceased production in 1962. The current retitled publication is IEEE Transactions on Information Theory.

Full Aims & Scope