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Proceedings of the IEEE

Issue 5 • Date May 1970

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Displaying Results 1 - 25 of 75
  • [Front cover and table of contents]

    Page(s): c1
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    Freely Available from IEEE
  • Scanning the issue

    Page(s): 607 - 609
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    Freely Available from IEEE
  • An introduction to the theory of the detection of signals in noise

    Page(s): 610 - 623
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    An introductory discussion is presented in the general field of detection theory, with particular emphasis on the problems of detecting signals in Gaussian noise and of estimating parameters of signals in Gaussian noise. View full abstract»

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  • Nonparametric detection

    Page(s): 623 - 631
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    This paper considers some of the simpler nonparametric detection schemes and compares their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense. In the one-input case, the nonparametric sign and Wilcoxon detectors are compared to the linear detector which is optimal for the detection of a dc signal of unknown amplitude in Gaussian noise. For two-input systems the nonparametric polarity coincidence correlator is compared to the system which is optimal for the detection of a common random Gaussian component in two-input Gaussian noises. The nonparametric detectors are shown to offer advantages in simplicity of implementation and in insensitivity to changes in input statistics while performing moderately well compared to the parametric detectors. More impressive results can be obtained with more complicated detectors utilizing nonlinear rank statistics. View full abstract»

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  • Decision analysis: Perspectives on inference, decision, and experimentation

    Page(s): 632 - 643
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    This paper illustrates by using a simple coin-tossing example how the new discipline of decision analysis sheds light on the perennial problems of inference, decision, and experimentation. The inference problem is first discussed from the classical viewpoints of maximum likelihood estimation and hypothesis testing, and then from the viewpoint of subjective probability and Bayesian updating. The problem is next placed in a decision setting to demonstrate how an estimate is related to the nature of the loss structure. Experimental possibilities are evaluated for the case where the size of the experiment must be determined a priori and for the case where experimentation can cease at any point. The decision-analysis philosophy allows consideration of all these problems within one philosophical and methodological framework. View full abstract»

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  • Performance limitations and error calculations for parameter estimation

    Page(s): 644 - 652
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    Error calculations cannot be carried out precisely when parameters are estimated which affect the observation nonlinearly. This paper summarizes the available approaches to studying performance and compares the resulting answers for a specific case. It is shown that the familiar Cramér-Rao lower bound on rms error yields an accurate answer only for large signal-to-noise ratios (SNR). For low SNR, lower bounds on rms error obtained by Ziv and Zakai give easily calculated and fairly tight answers. Rate distortion theory gives a lower bound on the error achievable with any system. The Barankin lower bound does not appear to give useful information as a computational tool. A technique for approximating the error can be used effectively for a large class of systems. With numerical integration, an upper bound obtained by Seidman gives a fairly tight answer. Recent work by Ziv gives bounds on the bias of estimators but, in general, these appear to be rather weak. Tighter results are obtained for maximum-likelihood estimators with certain symmetry conditions. Applying these techniques makes it possible to locate the threshold level to within a few decibels of channel signal-to-noise ratio. Further, these calculations can be easily carried out for any system. View full abstract»

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  • Applications of state-variable techniques in detection theory

    Page(s): 653 - 669
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    The central issue in detection theory is that of detecting known or random signals in the presence of random noise. The detailed problem description depends on the physical situation of interest. In most of the original work on detection theory the random processes were modeled as Gaussian processes and characterized by their covariance function. In many cases the solution for the optimum detector is expressed in terms of an integral equation which is difficult to solve. In this paper we demonstrate how to formulate and solve detection theory problems using state-variable techniques. These techniques enable us to obtain complete solutions to almost all problems of interest. In addition, they offer new insights into the problems. We first formulate our basic state-variable model for real and complex random processes. We then study five applications of state-variable techniques. The first application is in the solution of linear homogeneous Fredholm equations. This problem arises whenever we want to find the eigenvalues and eigenfunction of a random process. The second application is the detection of a slowly fluctuating point target in the presence of colored noise. The third application is the detection of Gaussian processes in Gaussian noise. The fourth application is detection of Doppler spread targets and communication over Doppler spread channels. In the final application, we introduce distributed state variables in order to study the detection of doubly spread targets. The goal of the paper is to demonstrate the importance of state-variable techniques in a wide variety of detection theory problems. View full abstract»

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  • Detection and estimation of signals in noise when one or both are non-Gaussian

    Page(s): 670 - 679
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    An examination is made of the basic principles and results of the theory of detection and estimation of signals in noise, which is not limited to the condition that the useful signal and noise be Gaussian and that the noise be additive. Formulas are obtained [(23) and (25)] for likelihood ratios which are useful in the Markovian as well as in the non-Markovian case. The results are specialized for the case of diffusion noise and fixed but unknown signal parameters, when it is possible to effectively utilize the theory of conditional Markov processes. Estimation by the quasi-linear theory is also discussed, the applicability of which is limited not by the Markovian condition, but by the condition of high a posteriori accuracy. In conclusion, a generalization is given of the theory for the case of adaptive detection and estimation, when the a priori information is replaced by learning. In this case, application of the theory of conditional Markov processes makes it possible to obtain, besides the previous equations of Gaussian approximation, similar equations for the unknown parameters. View full abstract»

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  • The innovations approach to detection and estimation theory

    Page(s): 680 - 695
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    Given a stochastic process, its innovations process will be defined as a white Gaussian noise process obtained from the original process by a causal and causally invertible transformation. The significance of such a representation, when it exists, is that statistical inference problems based on observation of the original process can be replaced by simpler problems based on white noise observations. Seven applications to linear and nonlinear least-squares estimation. Gaussian and non-Gaussian detection problems, solution of Fredholm integral equations, and the calculation of mutual information, will be described. The major new results are summarized in seven theorems. Some powerful mathematical tools will be introduced, but emphasis will be placed on the considerable physical significance of the results. View full abstract»

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  • Multidimensional detection and extraction of signals in random media

    Page(s): 696 - 706
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    An approach to the general problem of detecting and extracting signals from random media with the help of multichannel (i.e., multidimensional) receivers is described, based on standard decision theory methods and stressing the key role of channel physics and geometry. The principal aim is to provide an illustrative outline of a unified treatment, emphasizing the interdisciplinary character of the methods used and the critical nature of the channel model for both optimal and suboptimal systems. Included is a discussion of system apertures (arrays), the dynamical equations of propagation in elastic media and for electromagnetic phenomena, scattering, ambient (self-) noise fields, preformed and adaptive beams, Poisson and Gaussian field statistics, and general methods for obtaining the statistical description of noise and signal fields. Two illustrative examples of some recent results are briefly considered, and a number of important current problems are described, whose solutions depend on the approach developed here. View full abstract»

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  • Parameter estimation in speech: A lesson in unorthodoxy

    Page(s): 707 - 712
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    The accurate estimation of both discrete and continuous parameters of speech signals has played a central role in speech processing and research. Interestingly, the most successful estimation procedures have often relied on intuition based on knowledge of speech signals and their production in the human vocal apparatus rather than routine applications of well-established theoretical methods. This experience in speech processing should serve as a reminder that a thorough understanding of the signal is paramount for successful analyses of real-world processes. View full abstract»

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  • Application of detection theory in psychophysics

    Page(s): 713 - 723
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    The paper reviews how current developments in detection theory have contributed to our understanding of human sensory processes. The first section of the paper emphasizes the methodological contributions of detection theory and how the theory is useful in the analysis of discrimination data. Next, a brief discussion of the substantive contribution of the theory in auditory research is considered. Energy detection, internal and external fluctuation, and some recent work using a Poisson model, illustrate these substantive applications of detection theory. View full abstract»

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  • Frequency discrimination in the auditory system: Place or periodicity mechanisms?

    Page(s): 723 - 730
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    The pattern of all-or-none firings in many sensory nerves can usefully be modeled as a set of sample functions from non-stationary random processes whose parameters are determined by the sensory stimulus. Given such a description, one can compare the parameter estimation, discrimination, or detection performance of a human observer (as measured behaviorally) with the computed limiting performance of an ideal observer operating on the same neural input. Such a comparison is carried out in detail for the discrimination in frequency of an auditory sinusoidal tone burst. The results suggest that the human listener behaves as if he ignored (at least for this class of sounds) the periodicity information in the auditory nerve pattern (resulting from the phase-locking of the firings to the stimulus), but made full effective use of the place information (resulting primarily, although not entirely, from the mechanical tuning of the inner ear). On the other hand, it is known that the auditory system can discriminate certain more complicated stimuli on the basis of periodicity information if that is the only cue available. A modification of the structure of an optimum sinusoidal frequency discrimination system is conjectured that seems to be, at least qualitatively, consistent with the available evidence. View full abstract»

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  • Sequential methods in radar detection

    Page(s): 731 - 743
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    Certain sequential tests of statistical hypotheses known as sequential probability ratio tests (SPRT) possess an optimum property that they can accelerate, on the average, the termination of the test or alternately execute the test in the same time with less error, or with the same error but on less distinguishable hypotheses than a fixed sample-size test. These properties are of practical importance when applied to the radar problem, but in the application of sequential methods to radar surveillance some modification of an SPRT is frequently necessary. In particular, design problems relating to phased array radars are considered. This paper reviews the problem of angle search constraints, existence of multiple resolution elements in range and velocity, possibility of a flexible allocation of pulses, and fluctuations of radar cross sections of targets. Representative numerical results are included to indicate what performance can be expected with the use of sequential methods. An attempt is made to present an integrated theoretical and practical picture. Key references are listed. View full abstract»

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  • Detection and estimation practices in radio and radar astronomy

    Page(s): 743 - 759
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    A review is given of detection and estimation methods in current use in radio and radar astronomy. Methods of determining position and brightness distribution of radio sources by narrow-beam antennas, interferometry or lunar occultations are discussed. Observational procedures for the estimation of frequency spectra are explained. The fundamental problem in radar astronomy, viz., that of mapping, is reviewed, and several methods for the removal of ambiguities are considered. Schemes for the determination of range and velocity of a planet are also described. View full abstract»

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  • Applications of detection and estimation theory to large array seismology

    Page(s): 760 - 770
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    The statistical theory of signal detection and estimation has been applied to problems in large array seismology. Using this theory the structure of the optimum detector for a known signal and long observation time in additive Gaussian noise is derived. The array processing filter employed by the optimum detector is known as the maximum-likelihood filter. This filter also has the property that it provides a minimum-variance unbiased estimate for the input signal when it is not known, which is the same as the maximum-likelihood estimate of the signal if the noise is a multidimensional Gaussian process. A series of experiments was performed using data from the large aperture seismic array to determine the effectiveness of the maximum-likelihood method relative to simpler methods such as beam-forming. These results provide significant conclusions regarding the design and processing of data from large seismic arrays. The conventional and high-resolution estimation of the frequency-wavenumber spectrum of the background microseismic noise is also presented. The diffuse structure of this spectrum is shown to aid in explaining the relative performance of array processing methods. View full abstract»

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  • Applications of space-time decision and estimation theory to antenna processing system design

    Page(s): 771 - 778
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    A mathematical solution to the problem of optimum radar target detection and parameter estimation in receiver noise and heavy clutter has been achieved by means of space-time decision theory. The theory leads to a conceptual design for an antenna processing system that is optimum in the sense that it makes least risk parameter estimates and least probability of error decisions. The system can be instrumented by separately demodulating the individual radiator outputs and feeding them simultaneously and in parallel to a digital computer, Hypothesis testing problems such as target detection are formulated by means of a generalized likelihood ratio test. Optimum mean-square estimation is carried out by instrumenting the mean of the parameter in question conditioned on the observed signal. With the aid of a priori statistics available or assumed, the a posteriori likelihood function is derived. From this function, the required generalized likelihood ratio hypothesis tests and parameter estimators are synthesized. Specific illustrations include systems for detection and angular location estimation for one or two targets in a clutter environment. Optimum tests as well as optimum and suboptimum estimators are realized as flow diagrams for computation by the special-purpose digital processor. View full abstract»

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  • Statistical detection for communication channels with intersymbol interference

    Page(s): 779 - 785
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    The optimum detector under a fixed delay constraint D is derived for channels having memory and additive noise. The resulting receiver is recursive and does not grow with the message length. Its structure is presented for linear channels (AM and PSK) with known (or estimated) impulse response and noise statistics. The intersymbol interference is assumed to extend for L sampling periods and the receiver is allowed a "look-ahead" at D future received samples. Simulation results using actual channel characteristics show the detector to outperform a transversal equalizer even for relatively small values of D. View full abstract»

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  • Junction-gate FET RF power amplifier

    Page(s): 789 - 790
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    A junction-gate power field-effect transistor of recent design has been found to yield greater than 25 watts CW at 30 MHz in two modes of circuit configuration. In this investigation, favorable characteristics are explored for potential device utility as a high-reliability low-distortion RF power amplifier. View full abstract»

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  • An avalanche photodiode with a tapered light-focusing fiber guide

    Page(s): 790 - 791
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    The light-receiving area of an avalanche photodiode has been effectively enlarged by means of a tapered light-focusing fiber guide. View full abstract»

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  • Visualization of internal structure by microwave holography

    Page(s): 791 - 792
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    Microwave holography was used for the visualization of an internal structure within a dielectric. Descriptions are given of 1) the preparation of the liquid crystal film to be used for mapping the microwave field, and 2) the application of the liquid crystal film in the fabrication of a microwave hologram to visualize the internal structure within a dielectric. View full abstract»

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  • The turn-on delay time of silicon p-n-p-n switches

    Page(s): 792 - 793
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    The turn-on delay time of silicon p-n-p-n switches has been experimentally shown to be inversely proportional to gate currents in excess of the threshold value. Based on the measurements of bidirectional p-n-p-n switches, it is demonstrated that p-n-p-n structures with remote gating have inherently longer turn-on delay times than those of the conventional construction having the gate lead attached to a base region. View full abstract»

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  • On the radar cross section of a dipole

    Page(s): 793 - 794
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    Literature references dealing with the radar cross section of a dipole target contain a possible source of confusion in that two definitions of cross section have been used. To clarify this situation, the radar cross section of a randomly oriented half-wave dipole is considered using both definitions. View full abstract»

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  • An active butterworth frequency discriminator

    Page(s): 795 - 796
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    An active realization for a bandpass maximally flat, linear amplitude filter is presented. The filter displays a linear amplitude rise with an increasing frequency change about a center point out to cutoff frequenoies beyond which the response falls off at a rate determined by the order of the filter. View full abstract»

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