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Showing papers on "White noise published in 1985"


Journal ArticleDOI
TL;DR: In this paper, the authors apply a newly developed statistical technique to time series of daily rates of return of 15 common stocks and show that the results suggest that daily stock returns are generated by a nonlinear process.
Abstract: This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect nonconstant skewness in the bispectrum. Hence if the test rejects constant skewness, a nonlinear process is implied. As a consequence, the test can distinguish between white noise and purely random noise. The results suggest that daily stock returns are generated by a nonlinear process.

279 citations


Journal ArticleDOI
TL;DR: It is shown that the proposed parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model provides bispectral estimates that are far superior to the conventional estimates in terms of bispectrals fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.
Abstract: Higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. Estimation of the bispectrum, which is a third-order spectrum, has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non-Gaussianness of processes. Existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model. The AR parameter estimates are obtained by solving the third-order recursion equations which may be Toeplitz in form but not symmetric. It is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.

275 citations


Journal ArticleDOI
TL;DR: In this article, a smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is presented, where the unknown white noise variances are hyperparameters of the AR coefficient distribution.
Abstract: A smoothness priors time varying AR coefficient model approach for the modeling of nonstationary in the covariance time series is shown. Smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each AR coefficient. The unknown white noise variances are hyperparameters of the AR coefficient distribution. The critical computation is of the likelihood of the hyperparameters of the Bayesian model. This computation is facilitated by a state-space representation Kalman filter implementation. The best difference equation order-best AR model order-best hyperparameter model locally in time is selected using the minimum AIC method. Also, an instantaneous spectral density is defined in terms of the instantaneous AR model coefficients and a smoothed estimate of the instantaneous time series variance. An earthquake record is analyzed. The changing spectral analysis of the original data and of simulations from a time varying AR coefficient model of that data are shown.

266 citations


Journal ArticleDOI
TL;DR: The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additiveoutput noise.
Abstract: Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.

244 citations


Journal ArticleDOI
01 Oct 1985
TL;DR: In this paper, it is shown that for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable.
Abstract: In this letter, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheodory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes, and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.

205 citations



Journal ArticleDOI
TL;DR: In this article, the authors compared the power spectra, estimated by the maximum entropy method and by a fast Fourier transform-based periodogram method, using simulated time series.
Abstract: Power spectra, estimated by the maximum entropy method and by a fast Fourier transform based periodogram method, are compared using simulated time series. The times series are computer generated by passing Gaussian white noise through low-pass filters with precisely defined magnitude response curves such that the output time series have power law spectra in a limited frequency range: P(f) = Af −p, f1 ≤ f ≤ f2. Ten different values of p between 0.5 and 5.0 are used. Using 4000 independent realizations of these simulated time series, it is shown that maximum entropy results are superior (usually greatly superior) to the periodogram results even when end-matching or windowing or both are used before the power spectra are estimated. Without the use of end-matching or windowing or both, the periodogram results are useless at best and very misleading at worst. For an application to geophysical data, a 5-min section of ionospheric scintillation data from the MARISAT satellite was chosen because it illustrates a transition from low-level background noise to moderate scintillation and another transition to fully saturated scintillation. This section was broken into 60 sections, each 10 s long and overlapped by 5 s. Order 5 Burg-MEM spectra from the raw data are compared with periodograms computed from end-matched and windowed data. The superiority of Burg-MEM rests largely in the smoothness of the spectrum: real changes in spectral shape are not obscured by meaningless detail.

115 citations


Journal ArticleDOI
TL;DR: In this article, a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence is introduced, and the efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided.
Abstract: In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided. Finally, we study the asymptotic relative efficiency of the proposed procedures with respect to their normal theory counterparts based on sample autocorrelations.

105 citations


Posted Content
TL;DR: In this paper, a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence is introduced, and the efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided.
Abstract: In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided. Finally, we study the asymptotic relative efficiency of the proposed procedures with respect to their normal theory counterparts based on sample autocorrelations.

102 citations


Journal ArticleDOI
TL;DR: A statistical analysis of fixed-point round off error is presented that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these conditions are not satisfied.
Abstract: Roundoff error after fixed-point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal. This paper presents a statistical analysis of fixed-point roundoff error that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these conditions are not satisfied. The results show that if the multiplier coefficient is expressed as a = N/M, where M is a positive integral power of two and N is an odd integer, then the errors generated by roundoff after multiplication can generally be modeled as uniformly distributed, white, and uncorrelated with the signal, if the signal has sufficiently wide bandwidth and has a dynamic range that extends over approximately M quantum steps. For narrow-band low-level signals, the roundoff error statistics can differ significantly from the uniform, white, uncorrelated model. In addition, these results show that statistical behavior of roundoff error can differ significantly from that of the quantization error that is generated when a continuous random variable is quantized.

89 citations


Journal ArticleDOI
TL;DR: In this paper, a simple theory for evaluating the several measures used to characterize the intermittency of fine-scale turbulence, and corroborates the theoretical results from comparison with experimental data, some of which are new.
Abstract: This paper presents a simple theory for evaluating the several measures used to characterize the intermittency of fine-scale turbulence, and corroborates the theoretical results from comparison with experimental data, some of which are new. The basic analytical tool is the envelope of the narrow-bandpass-filtered turbulent signal, defined via its Hilbert transform and the analytic signal. The contribution of this paper is twofold. First, it correctly identifies the roles played by the filter characteristics (such as the bandwidth) in determining the intermittency factor, the width of the active regions (pulses) in narrow-bandpass-filtered turbulent signals, and the pulse frequency; it also reveals that all dynamical characteristics of the signal enter indirectly through the peak pulse frequency and the threshold setting. Secondly, the theory suggests that, in the far-dissipation range, the most important feature of signals exhibiting internal intermittency is the stronger-than-algebraic roll-off of the spectral density in that region; it is argued that this feature of turbulence essentially determines the peak pulse frequency in that region. The theory is incomplete in that it does not show how the threshold setting depends on the signal dynamics, but here the discussion is supplemented by experimental data.

Journal ArticleDOI
TL;DR: In this paper, a linear predictor is proposed to predict unobserved values of a linear process with infinite variance, which minimizes the dispersion (suitably defined) of the error distribution, which can be interpreted as minimizing an appropriately defined l α -distance between the predictor and the random variable to be predicted.

Journal ArticleDOI
TL;DR: In this paper, the second moments of autocorrelations were studied for both Gaussian and non-Gaussian series, and bounds for the variances and covariances of sample autorrelations from an arbitrary random sequence were derived.

Journal ArticleDOI
TL;DR: A scheme is analyzed which can improve the detection performance of FH waveforms in wide-band additive Gaussian noise (AWGN) using samples from the autocorrelation domain, albeit inferior to the optimal likelihood-ratio test, has the advantage of reduced complexity.
Abstract: Interception of frequency-hopping (FH) waveforms is commonly achieved by using a set of radiometers (energy detectors) that individually energy-detect subbands of the total spread bandwidth of the suspected transmission. In this paper, a scheme is analyzed which can improve the detection performance of FH waveforms in wide-band additive Gaussian noise (AWGN) using samples from the autocorrelation domain. It is shown that, under fairly general operational assumptions, an appreciable gain in decision signal-to-noise ratio (SNR) can be achieved over that of the radiometer. This gain is proportional to \gamma_{H}^{2} where \gamma _{H} is the hop SNR. The proposed algorithm, albeit inferior to the optimal likelihood-ratio test, has the advantage of reduced complexity. The overall approach has been motivated by the recent implementational feasibility of large time-bandwidth-product real-time correlators such as surface-acoustic wave devices (SAWD's).

Journal ArticleDOI
TL;DR: The comparison shows that the loss in the performance of DS/SSMA systems due to noncoherent reception can be considerably larger than the loss incurred to noncoberent single-user systems operating in additive Gaussian noise.
Abstract: The performance of noncoherent reception in direct-sequence spread-spectrum multiple-access communications systems is investigated for additive white Gaussian noise channels. Analytical and numerical results on the probability of error are presented for binary and M -ary frequency-shift-keying data modulation with noncoherent demodulation and differential-phase-shift-keying data modulation with differentiallycoherent demodulation. Both synchronous and asynchronous systems are analyzed. Systems which employ deterministic as well as random signature sequences are considered. The multiple access capability of noncoherent DS/SS systems is evaluated and compared to that of coherent DS/SS systems with the same parameters. The comparison shows that the loss in the performance of DS/SSMA systems due to noncoherent reception can be considerably larger than the loss incurred to noncoberent single-user systems operating in additive Gaussian noise.

Journal ArticleDOI
TL;DR: In this paper, a large number of highly robust and reliable thin film DC SQUIDs have been designed and fabricated which have excellent low frequency noise properties and showed that improvements in the performance of these devices in the white noise region can be obtained without sacrificing the low frequency resolution.
Abstract: A large number of highly robust and reliable thin film DC SQUIDs have been designed and fabricated which have excellent low frequency noise properties. Measurements performed on isolated devices have yielded a limit on the low frequency (1/f) flux noise component which is at least a factor of 60 below the average value reported for devices of this kind. The corresponding energy factor in the white noise region is 770 h at 0.1 Hz. The input coil inductance is 0.7 μH and the coupling efficiency α = 0.9. The substantial reduction of the low frequency noise in these SQUIDs demonstrates that improvements in the performance of these devices in the white noise region can be obtained without sacrificing the low frequency resolution.

Proceedings ArticleDOI
01 Dec 1985
TL;DR: In this paper, the optimal projection equations for fixed-order dynamic compensation in the presence of state-, control-and measurement-dependent noise were derived for high-order systems with parameter uncertainties.
Abstract: The Optimal Projection/Maximum Entropy approach to designing low-order controllers for high-order systems with parameter uncertainties is reviewed. The philosophy of representing uncertain parameters by means of Stratonovich multiplicative white noise is motivated by means of the Maximum Entropy Principle of Jaynes and statistical analysis of modal systems. The main result, the optimal projection equations for fixed-order dynamic compensation in the presence of state-, control- and measurement-dependent noise, represents a fundamental generalization of classical LQG theory.

Journal ArticleDOI
TL;DR: In this article, the average probability of bit error for a binary CPSK signal on an Earth-space link in the presence of scintillation fading and additive white Gaussian noise is derived.
Abstract: Theoretical estimates are derived of the average probability 〈Pb〉 of bit error rate that would occur for a binary CPSK signal on an Earth-space link in the presence of scintillation fading and additive white Gaussian noise. Strong scintillations are shown to produce a significant degradation in 〈Pb〉. Experimental results of the signal amplitude distribution obtained on a 7.1° elevation satellite downlink lead to values of 〈Pb〉 against 〈Eb/No〉 which agree well with the results obtained using the theoretical Moulsley-Vilar distribution (1982).

Journal ArticleDOI
TL;DR: The performance of synchronous and asynchronous hybrid direct-sequence/slow-frequency-hopped spread-spectrum multiple- access communications over additive white Gaussian noise channels is examined and it is shown that the multiple-access capability of hybrid spread-Spectrum is superior to that of pure frequency-hopping spread- Spectrum.
Abstract: The performance of synchronous and asynchronous hybrid direct-sequence/slow-frequency-hopped spread-spectrum multiple-access communications over additive white Gaussian noise channels is examined. Systems employing binary or quaternary phase-shift-keying modulation with coherent demodulation are investigated. Both deterministic and random signature sequences and frequency-hopping patterns are considered and several possible assignments for them are discussed. It is shown that the multiple-access capability of hybrid spread-spectrum is superior to that of pure frequency-hopped spread-spectrum, and inferior to that of pure direct-sequence spread-spectrum for systems with identical bandwidth expansion which employ the same data modulation and demodulation scheme and random hopping patterns and signature sequences.

Journal ArticleDOI
TL;DR: In this article, a detection procedure of such a segmentation based on the pseudo-Wigner estimates is presented, which is known to be uncorrelated estimates of the Wigner-Ville spectrum for neighboured, appropriately spaced frequencies.

Journal ArticleDOI
TL;DR: The representation of the EEG time series as a superposition of the resonant modes with characteristic decay factors seems a valuable method of the analysis of the signal, since it offers high reduction of the data to the few parameters of a clear physiological meaning.
Abstract: EEG time series were modeled as an output of the linear filter driven by white noise. Parameters describing the signal were determined in a way fulfilling the maximum entropy principle. Transfer function and the impulse response function were found. The solutions of the differential equations describing the system have the form of the damped oscillatory modes. The representation of the EEG time series as a superposition of the resonant modes with characteristic decay factors seems a valuable method of the analysis of the signal, since it offers high reduction of the data to the few parameters of a clear physiological meaning.


Journal ArticleDOI
TL;DR: A method to obtain noise-optimal state-space structures for fixed error feedback coefficients, starting from noise optimal structures in absence of error feedback (the Mullis and Roberts Structures), is outlined.
Abstract: A new scheme for shaping the error spectrum in state-space digital filter structures is proposed. The scheme is based on the application of diagonal second-order error feedback, and can be used in any arbitrary state-space structure having arbitrary order. A method to obtain noise-optimal state-space structures for fixed error feedback coefficients, starting from noise optimal structures in absence of error feedback (the Mullis and Roberts Structures), is also outlined. This optimization is based on the theory of continuous equivalence for state-space structures.

Proceedings ArticleDOI
01 Apr 1985
TL;DR: An outline of the derivation of the approximate probability density of the SNR for this adaptive detector is presented, assuming that the noise consists of a strong gaussian rank-one-covariance interference component plus a component of white gaussian background noise.
Abstract: The main advantage of our previously presented [10] principal-component method of adaptive detection, in comparison with the method based on the inverse of the estimated covariance matrix, is that much less data is required to produce a given, needed level of SNR with high probability. In this paper we present an outline of the derivation of the approximate probability density of the SNR for this adaptive detector. To simplify the derivation we assume that the noise consists of a strong gaussian rank-one-covariance interference component plus a component of white gaussian background noise. The approximations and the final probability density are tested through simulation.

Journal ArticleDOI
TL;DR: In this paper, the asymptotic behavior of infinite-dimensional discrete linear systems driven by white noise is considered, and mean square stability conditions are investigated, including a comparison with the deterministic stability problem.
Abstract: The asymptotic behaviour for infinite-dimensional discrete linear systems driven by white noise is considered in this paper. Both the evolution and convergence of the state correlation operators sequence are analysed. Mean square stability conditions are investigated, including a comparison with the deterministic stability problem. The particular case of compact operators is considered in some detail.

Journal ArticleDOI
TL;DR: The implementation and performance of wide-band detectors for direct-sequence and time-hopping spread-spectrum waveforms in the presence of additive white Gaussian noise are considered, and the performance penalty incurred when going from optimal to suboptimal detector structures is considered.
Abstract: The implementation and performance of wide-band detectors for direct-sequence and time-hopping spread-spectrum waveforms in the presence of additive white Gaussian noise are considered in this paper. Of interest here is the performance penalty incurred when going from optimal to suboptimal detector structures. In both cases, performance is quantified by appropriately defined distance measures and is ultimately compared to that of the simplest hypothesis-discriminating device, namely, the energy detector (radiometer).

Journal ArticleDOI
TL;DR: In this article, simple approximate formulae are introduced for the average and the standard deviation of the peak factor of stationary Gaussian processes, taking into account the bandwidth of the process and are based on the assumption that the extreme point process is Markovian.

Proceedings ArticleDOI
01 Apr 1985
TL;DR: A new adaptive filter structure is introduced that permits a closer placement of the transducers and that allows the cancellation of noise in the presence of crosstalk.
Abstract: The application of adaptive filters in noise cancelling often requires the relative placement of the two transducers at a distance that necessitates a large order filter in order to obtain an adequate output signal-to-noise ratio. A new adaptive filter structure is introduced that permits a closer placement of the transducers and that allows the cancellation of noise in the presence of crosstalk. Algorithms are developed for the new transversal and lattice structures. Simulations show considerable improvement in mean-square error over that obtained with standard noise cancelling algorithms.

Journal ArticleDOI
TL;DR: Performance on the semantic processing test was impaired by intermittent, unpredictable noise, but this noise had no effect on the syntactic reasoning test, suggesting the importance of considering the effects of meaningful noise rather than just examining white noise of different intensities.

Book ChapterDOI
01 Jan 1985
TL;DR: In this article, random vibration of Bresse-Timoshenko beams, with shear deformation and rotary inertia taken into account, is studied, and two types of excitation are considered: spacewise white noise and concentrated point loading.
Abstract: Random vibration of Bresse-Timoshenko beams, with shear deformation and rotary inertia taken into account, is studied. Two types of excitation are considered — distributed loading represented by spacewise white noise, and concentrated point loading. Timewise, both excitations are given by band-limited white noise with lower and upper cutoff frequencies. When the lower cutoff frequency vanishes, the lower modes of vibration play a decisive role, and classical and nonclassical theories yield coincident or close results; if the lower cutoff frequency is such that mostly higher modes are excited, the difference between predictions by these theories, may reach 50%.