Showing papers on "White noise published in 1977"
TL;DR: A necessary and sufficient condition is given to model the output of a quantizer as an infinite-precision input and an additive, uniform, white noise.
Abstract: In this paper, a necessary and sufficient condition is given to model the output of a quantizer as an infinite-precision input and an additive, uniform, white noise. The statistical properties of the quantization error are studied, and a detailed analysis for Gaussian distributed inputs is given.
492 citations
TL;DR: In this paper, a canonical transformation of a k-dimensional stationary autoregressive process is proposed, where the components of the transformed process are ordered from least predictable to most predictable.
Abstract: : This paper proposes a canonical transformation of a k dimensional stationary autoregressive process. The components of the transformed process are ordered from least predictable to most predictable. The least predictable components are often nearly white noise and the most predictable can be nearly nonstationary. Transformed variables which are white noise can reflect relationships which may be associated with or point to economic or physical laws. A 5-variate example is given.
361 citations
TL;DR: In this paper, an experimental technique for the determination of normal acoustic properties in a tube, including the effect of mean flow, was presented, where two stationary, wall-mounted microphones measure the sound pressure at arbitrary but known positions in the tube.
Abstract: An experimental technique is presented for the determination of normal acoustic properties in a tube, including the effect of mean flow. An acoustic source is driven by Gaussian white noise to produce a randomly fluctuating sound field in a tube terminated by the system under investigation. Two stationary, wall‐mounted microphones measure the sound pressure at arbitrary but known positions in the tube. Theory is developed, including the effect of mean flow, showing that the incident‐ and reflected‐wave spectra, and the phase angle between the incident and reflected waves, can be determined from measurement of the auto‐ and cross‐spectra of the two microphone signals. Expressions for the normal specific acoustic impedance and the reflection coefficient of the tube termination are developed for a random sound field in the tube. Three no‐flow test cases are evaluated using the two‐microphone random‐excitation technique: a closed tube of specified length, an open, unbaffled tube of specified length, and a pro...
318 citations
TL;DR: In this article, the first two power spectrum moments from the pulse pair covariance are analyzed and the mean frequency estimation from interlaced pulse pairs is compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.
Abstract: Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.
203 citations
TL;DR: In this article, a Kalman filtering approach is proposed to obtain optimal smoothed estimates of the so-called reflection coefficient sequence, which contains important information about subsurface geometry.
Abstract: This paper is motivated by a problem from seismic data processing in oil exploration. We develop a Kalman filtering approach to obtaining optimal smoothed estimates of the so-called reflection coefficient sequence. This sequence contains important information about subsurface geometry. Our problem is shown to be equivalent to that of estimating white-plant noise for a linear dynamic system. By means of the equations which are derived herein, it is possible to compute fixed-interval, fixed-point, or fixed-lag optimal smoothed estimates of the reflection coefficient sequence, as well as respective error covariance-matrix information. Our optimal estimators are compared with an ad hoc "prediction error filter," (PEF) which has recently been reported on in the geophysics literature. We show that one of our estimators performs at least as well as, and in most cases, better than the prediction error filter. Simulation results are given which support and illustrate the theoretical developments.
192 citations
TL;DR: In this paper, a new computational algorithm for the partial correlation coefficients of a linear system given the covariance of its output when excited by a white input noise was proposed. But the proposed algorithm does not make use of the usual parameters in the linear prediction recursion.
Abstract: This paper introduces a new computational algorithm for the partial correlation coefficients of a linear system given the covariance of its output when excited by a white input noise. Although derived from Levinson's well-known procedure, the proposed algorithm does not make use of the usual parameters in the linear prediction recursion. It may be implemented using fixed point arithmetics. Application to speech waves is emphasized.
170 citations
TL;DR: In this paper, the difference between the two most popular trend removal methods, first differences and linear least squares regression, is analyzed and the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion.
Abstract: This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the spectral density function (SDF) of these residuals relative to that of a white noise series would be exaggerated at the high frequency portion and attenuated at the low frequency portion. On the other hand, we show that the regression residuals from the linear detrending of a random walk series would contain large positive autocorrelations in the first few lags. Relative to that of white noises, the SDF of the regression residuals would be exaggerated at the low frequency portion and attenuated at the high frequency portion.
111 citations
TL;DR: In this paper, an unnecessary constraint is imposed during the minimization of the prediction error power, and when the constraint is relaxed and a lighter one imposed, the error power decreases and the problem is solved.
Abstract: Under certain conditions, Burg maximum entropy spectra of sampled sine waves, in the presence of additive Gaussian white noise, show either spontaneous line splitting (at low noise levels) or appreciable frequency shifting (at moderate noise levels). This difficulty arises because an unnecessary constraint is imposed during the minimization of the prediction error power. When the constraint is relaxed and a lighter one imposed, the error power decreases and the problem is solved. The nature of the constraint is discussed, and the mathematical details of the new method are presented. The new method is verified by using a few simple test cases in which spontaneous line splitting is healed or frequency shifting is reduced drastically (Fougere, 1975).
105 citations
09 May 1977
TL;DR: In this article, the two-sinusoid frequency resolution of conventional Fourier, autoregressive (AR), and a special ARMA power spectral density (PSD) estimators is considered.
Abstract: The two-sinusoid frequency resolution of conventional Fourier, autoregressive (AR), and a special autoregressive-moving average (ARMA) power spectral density (PSD) estimators is considered in this paper. The conventional Fourier spectrum analysis methods have resolutions which are, on the average, roughly the reciprocal of the observation interval. However, for any particular case of two sinusoids of some initial phases, the resolution may be much greater or much less than the average resolution. The special ARMA PSD estimator can, in principle, perfectly resolve any two sinusoids if the autocorrelation function is perfectly known. The AR spectral estimate has a resolution which varies as a function of signal-to-noise ratio (SNR) from that of the conventional Fourier methods at low SNB to that of the special ARMA method of high SNR. A signal power estimation and a noise power cancellation technique is also presented.
79 citations
TL;DR: In this paper, the authors present a brief qualitative discussion of Kalman filtering as contrasted with Wiener filtering, since the Kalman filter is an integral element in their new fast optimal white-noise estimators.
Abstract: We present a brief qualitative discussion of Kalman filtering as contrasted with Wiener filtering, since the Kalman filter is an integral element in our new fast optimal white-noise estimators. Additionally, we present two fast algorithms, one of which is shown to be very efficient for calculating fixed-interval estimates of the reflection coefficient sequence, the other of which is shown to be very efficient for calculating either fixed-point or fixed-lag estimates of that sequence. Detailed operation counts are given which support these claims. Flow charts are also given for the Kalman filter and the two new fast smoothing algorithms.
TL;DR: Two simple error spectrum shaping quantizers are presented, one to be used with narrow-band low- pass filters and the other with high-pass filters.
Abstract: The error introduced by zero memory quantizers can usually be modeled by an additive white noise component. By incorporating feedback and additional memory elements to these quantizers, it is possible to shape the error spectrum to advantage. Two simple error spectrum shaping quantizers are presented, one to be used with narrow-band low-pass filters and the other with high-pass filters. Simulation examples are presented where the reduction in roundoff errors is equivalent to three bits of data.
TL;DR: In this paper, the authors consider discrete-parameter stochastic processes that are the output of a nonlinear filter driven by white noise, and derive estimates of the unknown coefficients in the transfer function and the noise variance, and investigate their asymptotic properties.
TL;DR: A two-dimensional discrete stochastic model for representing images is developed that has lower mean square error, compared to a standard autoregressive Markov representation, and application to linear filtering of images degraded by white noise leads to scalar recursive filtering equations requiring only 0(N2log2N) computations.
Abstract: A two-dimensional discrete stochastic model for representing images is developed. This representation has lower mean square error, compared to a standard autoregressive Markov representation. Application of the model to linear filtering of images degraded by white noise leads to scalar recursive filtering equations requiring only 0(N2log 2 N) computations for N x N images. The filter algorithm is a hybrid algorithm where the image is transformed along one dimension and spatially filtered, recursively, in the other. Examples on a 255 X 255 image are given.
TL;DR: Tactile sensilla of the trochanteral hair plate in the coxotrochanterals joint of the cockroach leg were stimulated by random (white noise) displacement and the afferent action potentials resulting from the stimulation were observed, suggesting that the functional description may correspond to a physical system with two parts.
Abstract: Tactile sensilla of the trochanteral hair plate in the coxotrochanteral joint of the cockroach leg were stimulated by random (white noise) displacement and the afferent action potentials resulting from the stimulation were observed. From the resulting signals, the first and second order frequency response functions between the stimulus and the response were computed, together with their inverse Fourier transforms, the time domain Wiener kernels. Analysis of these results shows that the behaviour of the receptor may be minimally accounted for by a cascade of two functional elements, where the first is a linear element affected by the past history of the input signal (memory) and the second is a nonlinear element with no memory. The behaviour of the linear element is very close to that of a time differentiator or velocity detector, while the nonlinear element behaves as a rectifier which transmits the velocity signal only during flexion of the limb. The results suggest that the functional description may correspond to a physical system with two parts. The element performing differentiation is probably a fluid cavity in the mechanical connection from the hair to the dendrite, and the element performing rectification is most likely to be found in the cell membrane of the dendrite.
TL;DR: The functional properties of the photoreceptor of Calliphora erythrocephala are studied through the white noise method using CSRS stimuli to develop a procedure for the optimal choice of the important test parameters.
Abstract: The functional properties of the photoreceptor of Calliphora erythrocephala are studied through the white noise method using CSRS stimuli. A procedure for the optimal choice of the important test parameters is also outlined, which allows the effective use of CSRS stimuli in biological system identification.
TL;DR: Adaptive mean-square error (mse) and maximum-likelihood detection (MLD) algorithms for a dual-channel digital communication system in the presence of interchannel interference and white Gaussian noise are presented.
Abstract: Adaptive mean-square error (mse) and maximum-likelihood detection (MLD) algorithms for a dual-channel digital communication system in the presence of interchannel interference and white Gaussian noise are presented. The mse algorithm forms estimates of the transmitted symbols from a linear combination of received symbols using weights that minimize the mse between transmitted and estimated symbols. The nonlinear MLD algorithm minimizes the probability of symbol error by maximizing the probability of the received signal samples on the two channels over ail possible transmitted symbol pairs. The probability of error is derived for the two algorithms when quadrature phase-shift keying (QPSK) is used as a modulation technique, and is compared with that of a dual-channel QPSK system having no compensation for the crosstalk.
TL;DR: A brief qualitative discussion of Kalman filtering as contrasted with Wiener filtering is presented, since the Kalman filter is an integral element in the authors' new fast optimal white-noise estimators.
Abstract: In the above paper,1 the following references were inadvertently left off the list of references.
TL;DR: In this article, an approximation to the stationary joint density function of the displacement and velocity response is derived for oscillators with non-linear damping, excited by white noise, by reducing the basic two-dimensional Fokker-Planck equation for the transition density function to a one-dimensional equation relating to the energy envelope of the response.
27 Dec 1977
TL;DR: In this article, it was shown that the dependence of minimum detectable contrast upon the diameter of the circle to be detected could be significantly different in the presence of CT noise than in that of white noise.
Abstract: If the standard filtered backprojection algorithm with a filter of the form g(f) = |f|h(f) is applied to noisy projections, all of which have a noise power spectral density (NPSD), Sproj(f), then the resulting computed tomographic (CT) reconstruction has a two dimensional NPSD of the form, S(f) ~ |f||h(f)|2 Sproj(f). For proper reconstruction, h(f) must approach a non-zero constant as f 0. Provided Sproj(f) is constant, i.e. white projection noise, the CT noise at low frequencies is supprbssbd by the |f| factor. This low frequency suppression results in a long range negative spatial correlation of the CT noise. If white noise is spatially averaged over a circle of diameter d, then the variance in the averaged values will behave as a2 ~ d-2. For CT noise the variance drops faster than d-2. Simple signal-to-noise ratio considerations suggest that the dependence of minimum detectable contrast upon the diameter of the circle to be detected could be significantly differ-ent in the presence of CT noise than in that of white noise. Simulated reconstructions of a suitable detectability pattern demonstrate these differences may not exist unless the image is spatially smoothed before observation. It is pointed out that the pixel width used in the image display should be from 1/3 to 1/2 the width of the point spread function in order to avoid discrete binning problems.
TL;DR: The technique relies on the introduction of a pseudo-random binary signal into the system of such low level as to be unnoticeable at the output terminals of the system under test.
Abstract: This paper presents a technique for the measurement of transfer functions of individual components and overall systems under normal operating conditions. The technique relies on the introduction of a pseudo-random binary signal into the system. The signal is of such low level as to be unnoticeable at the output terminals of the system under test. Test results obtained on a 40 MW alternator and its associated AVR are described.
TL;DR: Signal detection theory analysis showed that diseriminability was higher in white noise than music and the setting of the cautious criterion showed an interaction between noise conditions and time on task.
Abstract: 12 subjects were tested twice on a one-hour visual vigilance task. 6 subjects first performed the teat accompanied by continuous white noise presented at 72 dB (A). The second time they performed the test it was accompanied by music, presented at a level previously calibrated to give an. average integrated output, over one hour, of 72 dB A. A further 6 subjects performed the two tests in the reverse order. Performance was analysed into hits and false alarms at 3 levels of confidence for report. Although raw score performance did not differ between conditions, a signal detection theory analysis showed that diseriminability was higher in white noise than music. The setting of the cautious criterion showed an interaction between noise conditions and time on task.
01 Jan 1977
TL;DR: It is shown that in the case of Gaussian noise there is a strong connexion between detection and estimation and some examples are given and some ideas on adaptive detection which needs estimation of a reference noise alone are presented.
Abstract: We present a general introduction to detection problems and estimation problems. In the first section we present shortly the two points of view, which are different. We show that in the case of Gaussian noise there is a strong connexion between detection and estimation and we give some examples. In particular we present some ideas on adaptive detection which needs estimation of a reference noise alone which is defined and used to give an example of detection receiver.
TL;DR: A method has been given to evaluate the error probability performance of PSK-type modulation with baseband pulses of finite overlap and mutually independent samples and it is shown that the error probabilities can be computed with any desired accuracy.
Abstract: One of the most interesting challenges in the field of digital radio is to generate and transmit signals which meet the spectral requirements and which have high detection efficiencies. The spectral efficiency of PSK-type modulation with overlapping baseband pulses is known to be better than that with nonoverlapping pulses of the same form; but, to our knowledge, no analysis is presently available to determine their detection efficiency. In this paper a method has been given to evaluate the error probability performance of PSK-type modulation with baseband pulses of finite overlap and mutually independent samples. It is shown that the error probability can be computed with any desired accuracy. For BPSK and for some typical transmit and receive filters and for a transparent channel corrupted by additive Gaussian noise we compare the detection efficiencies when the baseband modulation pulses have zero and nonzero overlap and when the transmitted signal satisfies the same spectral requirement. The nonoverlapping rectangular signaling is shown to be superior to overlapping raised-cosine signaling, but the differential degradation is less than 0.8 dB if the twosided 99-percent bandwidth W 99 satisfies 1.1/T \leq W_{99}\leq 1.6/T . The analytical results presented here for a binary system can be extended with minor modifications to any M -ary PSK system, M > 2 .
TL;DR: In this paper, a detailed description of coefficient quantization errors of the distributed arithmetic is given, which means a recently introduced technique for the realization of the inner product of two vectors where conventional multipliers and adders are replaced by a memory and an accumulator.
Abstract: This paper gives a detailed description of coefficient quantization errors of the distributed arithmetic, which means a recently introduced technique for the realization of the inner product of two vectors where conventional multipliers and adders are replaced by a memory and an accumulator. For systems excited by uniformly distributed white noise, an expression for the total power of the output error is derived. It may be compared with an earlier error analysis which, as will be shown, is too pessimistic for small vector lengths. In that case the total round-off error is partly correlated with the input signals while for large vector lengths usual errors due to the quantization of individual coefficients vanish and thus the total error can be described by an independent noise source at the output.
TL;DR: A FORTRAN IV computer program is presented which fits up to three exponential terms and a constant to experimental data according to a least-squares criterion and was tried out on artificially generated three-exponential curves with added white noise.
TL;DR: In this paper, the average partition function for an electron moving in a Gaussian random potential is computed, with a trial action like that in Feynman's polaron theory.
Abstract: We compute the average partition function for an electron moving in a Gaussian random potential. A path integral formulation is used, with a trial action like that in Feynman's polaron theory. We compute the variational bound as well as the first correction in a systematic cumulant expansion. The results are checked against exact formulas for the onedimensional white noise problem. The density of states in the low-energy tail has the correct exponential energy dependence, and energy-dependent prefactor to within a few percent. In addition, the partition function goes over smoothly to the perturbation theory result at high temperatures.