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Showing papers on "White noise published in 1987"


Journal ArticleDOI
TL;DR: It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint.
Abstract: Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.

1,851 citations


Book
17 Dec 1987
TL;DR: This book contains a unified treatment of a class of problems of signal detection theory which is not required to have Gaussian probability functions in its statistical description, and which allow for formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification.
Abstract: This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi tive noise which is not required to have Gaussian probability den sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type."

767 citations


Journal ArticleDOI
TL;DR: In this article, the power of tests for distinguishing between fractional Gaussian noise and white noise of a first-order autoregressive process was investigated, based on the beta-optimal principle, local optimality and rescaled range test.
Abstract: SUMMARY We consider the power of tests for distinguishing between fractional Gaussian noise and white noise of a first-order autoregressive process. Our tests are based on the beta-optimal principle (Davies, 1969), local optimality and the rescaled range test.

548 citations


Journal ArticleDOI
TL;DR: An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error.
Abstract: Binary direct-sequence spread-spectrum multiple-access communications, an additive white Gaussian noise channel, and a coherent correlation receiver are considered. An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined. The expression is used to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error. The bounds, which are obtained without making a Gaussian approximation, are compared to results obtained using a Gaussian approximation. The effects of transmitter power, the length of the signature sequences, and the number of interfering transmitters are illustrated. Each transmitter is assumed to have the same power, although the general approach can accommodate the case of transmitters with unequal powers.

402 citations


Book
01 Jan 1987
TL;DR: In this article, the FIR Linear Combiner Number Guessing Games Single-Integer Guessing Game Multiple-Integer Games Multiple Real Numbers Guessing games Adaptive Filter Algorithm Interpretation AN ANALYTICAL FRAMEWORK for DEVELOPNG ADAPTIVE ALGORITHMS: Background and Direction The Least Squares Problem Basic Formulation Reduction to the Normal Equations Direct Solution to the Optimal Vector The Meaning of P and P Examples Matching a Pure Delay Matching an Rotated Phasor Two Solution Technique Direct Inversion Iterative App
Abstract: THE NEED FOR ADAPTIVE FILTERING: Removal of Power Line Hum From Medical Instruments Adaptive Differential Pulse Code Modulation Equalization of Troposcatter Communication Signals Generality and Commonality BASIC PRINCIPLES OF ADAPTIVE FILTERING: The FIR Linear Combiner Number Guessing Games Single-Integer Guessing Games Multiple- Integer Guessing Games Multiple Real Numbers Guessing Games Adaptive Filter Algorithm Interpretation AN ANALYTICAL FRAMEWORK FOR DEVELOPNG ADAPTIVE ALGORITHMS: Background and Direction The Least Squares Problem Basic Formulation Reduction to the Normal Equations Direct Solution to the Optimal Vector The Meaning of P and P Examples Matching a Pure Delay Matching a Rotated Phasor Two Solution Technique Direct Inversion Iterative Approximation Computational Comparisons Consolidation The Least Mean Square Problem Formulation A Brief Review of Stochastic Process Ensemble Averages An Example Stationarity The Concept of White Noise.

383 citations


Journal ArticleDOI
TL;DR: The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered and a least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed.
Abstract: The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered The system is not restricted to be minimum phase, and it is allowed to contain all-pass components A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed Knowledge of the probability distribution of the driving noise is not required An order determination criterion that is a modification of the Akaike information criterion is also proposed Strong consistency of the proposed estimator is proved under certain sufficient conditions Simulation results are presented to illustrate the method

241 citations


Journal ArticleDOI
TL;DR: In this article, a time-domain statistical approach for power-law spectra has been proposed, which yields an alternative estimation method for most of the important random powerlaw processes encountered.
Abstract: Since a measurement is no better than its uncertainty, specifying the uncertainty is a very important part of metrology. One is inclined to believe that the fundamental constants in physics are invariant with time and that they are the foundation upon which to build internationl system (SI) standards and metrology. Therefore clearly specifying uncertainties for these physical invariants at state-of-the-art levels should be one of the principal goals of metrology. However, by the very act of observing some physical quantity we may perturb the standard, thus introducing uncertainties. The random deviations in a series of observations may be caused by the measurement system, by environmental coupling or by intrinsic deviations in the standard. For these reasons and because correlated random noise is as commonly occurring in nature as uncorrelated random noise, the universal use of the classical variance, and the standard deviation of the mean may cloud rather than clarify questions regarding uncertainties; i.e., these measures are well behaved only for random uncorrelated deviations (white noise), and white noise is typically a subset of the spectrum of observed deviations. The assumption that each measurement in a series is independent because the measurements are taken at different times should be called into question if, in fact, the series is not random and uncorrelated, i.e., does not have a white spectrum. In this paper, studies of frequency standards, standard-volt cells, and gauge blocks provide examples of long-term random-correlated time series which indicate behavior that is not “white” (not random and uncorrelated). This paper outlines and illustrates a straightforward time-domain statistical approach, which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations, the statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures, e.g., as outlined in the paper.

201 citations


PatentDOI
TL;DR: In this article, two loudspeakers are driven by signals derived from a reference signal x(n) by adaptive filtering carried out by a programmed microprocessor and memory unit, which adapts the filtering in dependence on error signals el(n), from four microphones (421, 422, 423 and 424) distributed in the passenger compartment.
Abstract: To reduce noise inside a motor car passenger compartment, two loudspeakers (371, 372) are driven by signals derived from a reference signal x(n) by adaptive filtering carried out by a programmed microprocessor and memory unit (36) which adapts the filtering in dependence on error signals el(n) from four microphones (421, 422, 423 and 424) distributed in the passenger compartment. Reference filtering coefficients are initially determined by analysis of finite impulse responses when white noise is acoustically coupled from the loudspeakers (37) to the microphones (42), a white noise generator (48) being coupled to the unit (36). The reference signal x(n) is restricted to one or more selected harmonics or subharmonics of the fundamental noise frequency by a filter (34) which tracks the selected frequency. The selected frequency may be obtained from a coil (31) in the ignition circuit of the vehicle.

174 citations


Journal ArticleDOI
TL;DR: These results show that in each case the high signal-to-noise maximum-likelihood rules have a performance nearly equal to that of the maximum- likelihood rules over a wide range of practically interesting signal- to- noise ratios (SNR's).
Abstract: The problem of locating a periodically inserted frame synchronization pattern in random data for a M -ary digital communication system operating over the additive white Gaussian noise channel is considered. The optimum maximum-likelihood decision rule, high signal-to-noise approximate maximum likelihood decision rule, and ordinary correlation decision rule for frame synchronization are derived for both coherent and noncoherent phase demodulation. A general lower bound on synchronization probability is derived for the coherent correlation rule. Monte Carlo computer simulations of all three decision rules, along with evaluations of the lower bound for the coherent correlation rule, were performed for the coherent MPSK, coherent, and noncoherent M ary orthogonal, and 16 QAM signaling schemes. These results show that in each case the high signal-to-noise maximum-likelihood rules have a performance nearly equal to that of the maximum-likelihood rules over a wide range of practically interesting signal-to-noise ratios (SNR's). These high SNR decision rules also provide significant performance improvement over the simple correlation rules. Moreover, they are much simpler to implement than the maximum-likelihood decision rules and, in fact, are no more complex than the correlation rules.

138 citations


Journal ArticleDOI
TL;DR: This paper analyzes a direct-sequence, spread-spectrum, multiple-access SSMA communication system which assigns a set of M orthogonal sequences to each user, and obtains approximations for the multiuser probability of error by using a Gaussian approximation for the multiple- access interference.
Abstract: This paper analyzes a direct-sequence, spread-spectrum, multiple-access (SSMA) communication system which assigns a set of M orthogonal sequences to each user. With all direct sequence SSMA systems, K users share a channel by phase modulating their transmissions with signature sequences. However, the users of our system transmit log_{2}M bits of information/sequence. This contrasts classical SSMA schemes which use a pair of antipodal sequences and transmit 1 bit/sequence. In this paper, we assume that the channel noise is a combination of additive white Gaussian noise (AWGN) and multiple-access interference. We employ the optimum (single-user) demodulator for orthogonal signals in Gaussian noise. The multiple-user performance of this receiver is analyzed. We obtain approximations for the multiuser probability of error by using a Gaussian approximation for the multiple-access interference. We also obtain an upper bound on the exact probability by using characteristic functions. Our SSMA system is Well suited for application at the lower radio frequencies. Therefore, a companion paper describes a realistic model for low-frequency radio noise, modifies the receiver to include a zero-memory nonlinearity, and studies the performance of the nonlinear receiver.

133 citations



Journal ArticleDOI
TL;DR: In this paper, an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series is presented, where the best k tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived.
Abstract: We present a new method for estimating the frequencies of the Earth's free oscillations. This method is an extension of the techniques of Thomson (1982) for finding the harmonic components of a time series. Optimal tapers for reducing the spectral leakage of decaying sinusoids immersed in white noise are derived. Multiplying the data by the best K tapers creates K time series. A decaying sinusoid model is fit to the K time series by a least squares procedure. A statistical F-test is performed to test the fit of the decaying sinusoid model, and thus determine the probability that there are coherent oscillations in the data. The F-test is performed at a number of chosen frequencies, producing a measure of the certainty that there is a decaying sinusoid at each frequency. We compare this method with the conventional technique employing a discrete Fourier transform of a cosine-tapered time-series. The multiple-taper method is found to be a more sensitive detector of decaying sinusoids in a time series contaminated by white noise.

Journal ArticleDOI
TL;DR: In this article, the influence of fluid-containing appendages on the dynamic response of multi-degree-of-freedom systems subjected to stochastic environmental loads, e.g., earthquakes, waves, or winds, is investigated.

Journal ArticleDOI
TL;DR: A simple method which allows nearly arbitrary specification of the quiescent response in a linearly constrained power minimization adaptation array and requires one additional linear constraint for both narrow-band and broad-band arrays.
Abstract: When an adaptive array operates in the presence of white noise only, the resulting beam pattern is referred to as the quiescent response. Typically, these patterns have mainlobe and sidelobe shapes differing from those designed for use in deterministic, nonadaptive arrays. This paper describes a simple method which allows nearly arbitrary specification of the quiescent response in a linearly constrained power minimization adaptation array. The only restriction on the quiescent is that it must meet the constraints defined for the adaptive array. Since many well-known deterministic designs such as Chebychev are not likely to meet the linear constraint conditions used in adaptive arrays for mainlobe and other pattern control functions, a procedure is presented which modifies the deterministic design to force it to meet the linear constraints in a least-squares manner. Once this has been accomplished, the methods outlined in this paper can be used to cause the modified deterministic design to become the quiescent response of the adaptive array. As a result, the adaptive array can be configured to closely resemble a deterministic array when the noise is white. Under conditions of correlated interference, or jamming, however, the response changes so as to effectively steer nulls in the appropriate directions. The method is based on the use of a generalized side-lobe canceller and requires one additional linear constraint for both narrow-band and broad-band arrays.

Journal ArticleDOI
TL;DR: In this article, a technique for the identification of arcing high impedance faults using burst noise signals at frequencies near the power system fundamental and low order harmonics is described, which can be differentiated from synchronous power system signals in the frequency bands of interest.
Abstract: Previous papers have described a method for the detection of arcing fallen distribution primiary conductor faults using the electrical noise in feeder current above 2kHz. While this method provided improved detection of such faults, this high frequency signal often would not propagate past capacitor banks. In the present paper, we describe a technique for the identification of arcing high impedance faults using burst noise signals at frequencies near the power system fundamental and low order harmonics. Arcing generates non-synchronous burst noise signals which approximate white noise, providing a signal which can be differentiated from synchronous power system signals in the frequency bands of interest. The primary advantage of monitoring frequencies near the fundamental is that this arcing fault signal at low frequencies will exhibit little attenuation from capacitor banks or other sources. This paper provides preliminary results that arcing faults can be detected effectively using frequency components below 60 Hz or between low order harmonics of 60 Hz. The technique is demonstrated through analysis of analog signals recorded during numerouis staged utility downed conductor tests.

Journal ArticleDOI
TL;DR: In this article, the authors describe and analyze a particular application of high duty-cycle time-division multiplexing to the separation and identification of signals from an interferometric sensor array.
Abstract: This paper describes and analyzes a particular application of high duty-cycle time-division multiplexing to the separation and identification of signals from an interferometric sensor array. Using the method discussed here, the coherence length of the laser is no longer a severe design constraint. Also, the source phase-induced intensity noise which limits some other multiplexing methods may be overcome, leading to a higher sensitivity. The arrays of all-passive remote sensors exhibit minimal crosstalk between sensors, and have downlead insensitivity. A synthetic heterodyne demodulation technique prevents environmentally induced signal fading. Analysis includes coupling ratios for all directional couplers in the system, signal and noise spectra, minimum detectable phase shift, and the effect of ac coupling on noise and crosstalk. An experimental all-fiber implementation of a two sensor array has yielded a measured sensitivity of approximately 10 μrad/ \sqrt{Hz} over a range of signal frequencies, and a crosstalk level of better than 55 dB.

Journal ArticleDOI
01 Jan 1987
TL;DR: In this article, the in-phase and quadrature components of the clutter echoes have been modelled to give a Weibull probability density function (PDF) of the amplitude and a uniform PDF of the phase.
Abstract: The paper deals with the problem of radar detection of a target echo embedded in Weibull clutter and white Gaussian noise (WGN). Relevant features of the paper, with respect to previous papers on the same subject, refer to the coherent nature of the Weibull process (that modelling the clutter) and of the processing chain. In more detail, the in-phase and quadrature components of the clutter echoes have been modelled to give a Weibull probability density function (PDF) of the amplitude and a uniform PDF of the phase. Any shape of the correlation function among consecutive clutter samples is also allowed in the model. The so called 'coherent Weibull clutter' (CWC) introduced in the paper represents a suitable generalisation of the conventional ?coherent Gaussian clutter? (CGC). The processing chain is also coherent, i.e. it operates on the in-phase and quadrature components of the signals. To derive a suitable processing scheme, we resort to the general theory of radar detection which applies to any type of PDF and autocorrelation function (ACF) of the target and clutter. Briefly, it is found that the processing scheme is based on two nonlinear estimators of the clutter samples in the two alternative hypotheses (i.e. H0 and H1 the fully fledged architecture being discussed in the paper. The detection processor turns out to be a suitable generalisation of that concerning the CGC case. A new family of processing schemes is derived in accordance with the statistical model assumed for the useful target. The following cases are covered: target known a priori, Swerling 0, 1 and 2 models, and partially fluctuating target. Attention is also paid to the interesting case of a target modelled as a coherent Weibull process. The detection of such a target against white Gaussian noise is worked out. The detection performance of the a

Journal ArticleDOI
TL;DR: A novel Langevin equation solely in terms of the laser intensity is obtained, which is proved fully describes the behavior of the intensity below, near, and somewhat above threshold, and for steady state the authors invoke and justify the ansatz of Hanggi et al. for treating Langevin equations containing strongly colored noise.
Abstract: A new Langevin equation for dye-laser fluctuations below and near threshold is used to obtain the intensity distribution function in closed form. The effect of strongly colored multiplicative pump noise is incorporated by means of an ansatz of Hanggi et al [Ph.ys. Rev. A 32, 695 (1985)] for an effective diffusion coefficient at steady states. Excellent agreement with the measurements of Lett, Short, and Mandel [Phys. Rev. Lett. 52, 341 (1984)] is obtained. I. INTRODUCTION Recent work on dye-laser noise has emphasized the simultaneous presence of additive quantum noise and multiplicative pump noise. Moreover, it has become apparent that the pump noise is not white but colored with a relatively long correlation time. Two experimental approaches have been used to characterize the noise parameters. Steady-state measurements of the normalized variance of the intensity fluctuations and the intensity autocorrelation function, ' and the first-passage-time technique have been used ' to determine these parameters. These measurements have produced refinements in the theoretical description of laser noise in terms of an augmented semiclassical laser model. The time evolution of the complex laser field is described by a Langevin equation containing both additive (spontaneous emission) noise ' and multiplicative (pump) noise. " ' When additive white noise and strongly colored pump noise are simultaneously present it is necessary to perform numerical Monte Carlo simulations in order to deduce the predictions of the theory for comparison with measurements. In this paper we will show that a detailed analysis of the steady-state measurements is possible which avoids time consuming simulations. This is possible because (a) we obtain a novel Langevin equation solely in terms of the laser intensity, which we prove fully describes the behavior of the intensity below, near, and somewhat above threshold, and (b) for steady state we invoke and justify the ansatz of Hanggi et at'. ' for treating Langevin equations containing strongly colored noise. Lett, Short, and Mandel observed a peak in the normalized variance of the intensity fluctuations as a function of mean intensity. They used the Monte Carlo procedure of Sancho et al. ' as applied to the laser problem by Dixit and Sahni, to fit their measurements. We have used our Langevin equation to obtain the steady-state probability distribution for the intensity with which we have also fit their data. This procedure is far simpler to implement than the Monte Carlo simulations. The agreement obtained among measurements, simulations, and our theory strongly supports both the Langevin intensity equation and the ansatz of Hanggi et al. ' for colored noise in steady-state situations.

Journal ArticleDOI
TL;DR: In this paper, a quantitative measure of topology -the genus of contours in a smoothed density distribution -was described and applied to numerical simulations of galaxy clustering, to a variety of three-dimensional toy models, and to a volume-limited sample of the CfA redshift survey.
Abstract: Many models for the formation of galaxies and large-scale structure assume a spectrum of random phase (Gaussian), small-amplitude density fluctuations as initial conditions. In such scenarios, the topology of the galaxy distribution on large scales relates directly to the topology of the initial density fluctuations. Here a quantitative measure of topology - the genus of contours in a smoothed density distribution - is described and applied to numerical simulations of galaxy clustering, to a variety of three-dimensional toy models, and to a volume-limited sample of the CfA redshift survey. For random phase distributions the genus of density contours exhibits a universal dependence on threshold density. The clustering simulations show that a smoothing length of 2-3 times the mass correlation length is sufficient to recover the topology of the initial fluctuations from the evolved galaxy distribution. Cold dark matter and white noise models retain a random phase topology at shorter smoothing lengths, but massive neutrino models develop a cellular topology.

Journal ArticleDOI
TL;DR: In this article, a near-white-noise input-output formalism was developed that does not require white noise assumptions and correlation formulas for outputs were developed, which enables account to be taken of reflections of near white noise inputs, and applied to the inhibition of atomic phase decays by squeezed light from a degenerate parametric amplifier incident upon a two-level atom.
Abstract: A near-white-noise input–output formalism is developed that does not require white-noise assumptions. In particular, correlation formulas for outputs are developed, which enables account to be taken of reflections of near-white-noise inputs. The methods are applied to the inhibition of atomic phase decays by squeezed light from a degenerate parametric amplifier incident upon a two-level atom, and modifications from previous work carried out in the extreme-white-noise limit are computed.


Journal ArticleDOI
Weiping Li1
TL;DR: It is shown that the Wigner distribution (WD) method of optimally detecting a chirp signal in white Gaussian noise is equivalent mathematically to a dechirp method.
Abstract: It is shown that the Wigner distribution (WD) method of optimally detecting a chirp signal in white Gaussian noise [1] is equivalent mathematically to a dechirp method.

Journal ArticleDOI
TL;DR: This paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown.
Abstract: This paper considers the estimation of the two close dominant frequencies in the signal when it is known a priori that the observation is a sum of two close sinusoids and an additive colored noise whose spectral density is unknown. Earlier attempts have assumed the additive noise to be independent. Next we develop decision rules for checking whether the observed signal has only one sinusoid or two close sinusoids. All of the earlier studies assumed that there are two close sinusoids in the signal. Another model discrimination problem considered is the determination of the causal structure of the observed periodicity. A rule is given to test whether the observation comes from a sinusoid plus additive noise, possible colored, or the observation comes from a stationary autoregressive model. We also present a numerical study showing the efficacy of the robust estimation procedure for estimating the two frequencies and the decision rules for checking the number of dominant frequencies and the causal mechanism. Finally, we compare the proposed method to well-known methods used for two close sinusoids in white noise.

Journal ArticleDOI
TL;DR: In this paper, a first-order Markov model for the correlation of the measurement errors on successive observations is used to estimate the effect of correlation on the time interval between measurements by a factor (1+a)/(1-a).
Abstract: For many tracking applications, the measurement errors onsuccessive observations are correlated. Using a first-order Markov model for the correlation, we present analytical expressions for the time-varying covariance and gains of an alpha-beta tracking filter.To a good approximation, the effect of correlation is to increase the time interval between measurements by a factor (1+a)/(1-a),where a is the coefficient of correlation between successive measurements.

Journal ArticleDOI
H. Wang1, M. Kaveh
TL;DR: It is shown that the detection and estimation performances of the practical coherent algorithm are close to those of the perfectly coherent processing, and that they are relatively insensitive with respect to a preliminary estimate of the angles used to effect an approximate coherence.
Abstract: This is the second part of a study which deals with the performance of multiple-source direction finding via signal-subspace processing [1]. An analytical evaluation of detection (determination of the number of sources) and direction estimation performance is presented for the coherent wide-band signal-subspace processing algorithm [2], which operates on the received array signals of large relative bandwidth. The probabilities of underestimating and overestimating the number of sources are derived, under asymptotic conditions and in the threshold regions, in terms of the choice of a penalty function and signal, noise, and array parameters for the cases of at most two closely spaced sources in spatially white noise. A scalar measure is used for the evaluation of the quality of the estimated signal subspaces. It is shown that the detection and estimation performances of the practical coherent algorithm are close to those of the perfectly coherent processing, and that they are relatively insensitive with respect to a preliminary estimate of the angles used to effect an approximate coherence.

Journal ArticleDOI
TL;DR: It is shown that the ML estimator of d(t) can be implemented in any of four canonical forms which, in general, are time-varying systems, and reduce to a generalized cross correlator for the special case treated in [1].
Abstract: This paper presents, for the first time, the exact theoretical solution to the problem of maximum-likelihood (ML) estimation of time-varying delay d(t) between a random signal s(t) received at one point in the presence of uncorrelated noise, and the time-delayed, scaled version αs(t - d(t)) of that signal received at another point in the presence of uncorrelated noise The signal is modeled as a sample function of a nonstationary Gaussian random process and the observation interval is arbitrary The analysis of this paper represents a generalization of that of Knapp and Carter [1], who derived the ML estimator for the case that the delay is constant, d(t) = d 0 , the signal process is stationary, and the received processes are observed over the infinite interval (-∞, +∞) We show that the ML estimator of d(t) can be implemented in any of four canonical forms which, in general, are time-varying systems We also show that our results reduce to a generalized cross correlator for the special case treated in [1]

Journal ArticleDOI
TL;DR: In this paper, the authors derived the Wiener kernels of the Volterra series with time ordered, triangular kernels, which describe coherence decays of particular density matrix elements.

Journal ArticleDOI
TL;DR: A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed and its performance is analyzed.
Abstract: We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.

Journal ArticleDOI
TL;DR: In this paper, it is argued that the two-component timing-noise power spectra of pulsars with composite spectra (namely, blue noise in high frequencies and red noise in low frequencies) could be caused by two related mechanisms.
Abstract: The mechanism by which the fluctuations in pulsar periods, known as the timing noise, are produced was investigated in the framework of the vortex creep theory. It is argued that the two-component timing-noise power spectra of pulsars with composite spectra (namely, blue noise in high frequencies and red noise in low frequencies) could be caused by two related mechanisms. It is proposed that the low-frequency component could be caused by the sudden change of current braking torque, which is perturbed by the microglitches. The perturbed torque will remain unchanged until the next microglitch; hence, the step-function-like variations in torque will give rise to a random walk in the frequency derivative (or red noise in the noise power spectra of the frequency derivative). 32 references.

Proceedings ArticleDOI
06 Apr 1987
TL;DR: A new and improved iterative speech enhancement technique based on spectral constraints is presented, which ensures more speech-like formant trajectories than those found in the unconstrained approach.
Abstract: A new and improved iterative speech enhancement technique based on spectral constraints is presented in this paper. The iterative technique, originally formulated by Lim and Oppenheim, attempts to solve for the maximum likelihood estimate of a speech waveform in additive white noise. The new approach applies inter- and intra-frame spectral constraints to ensure convergence to reasonable values and hence improve speech quality. An extremely efficient technique for applying these constraints is in the use of line spectral pair (LSP) coefficients. The inter-frame constraints ensures more speech-like formant trajectories than those found in the unconstrained approach. Results from speech degraded by additive white Gaussian noise show noticeable quality improvement.