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The effect of stimulus repetition was investigated in a speech identification task where intelligibility was lowered not by white noise added to the audio waveform but by ‘structural’ noise added to the spectrum parameters. Several aspects of the results argue for the improvement in intelligibility between one and two presentations being due not to statistical averaging over internal or external noise, but to increased perceptual selectivity under the influence of the first presentation's stimulus properties.

The white noise level of space-charge-limited current (SCLC) of holes in a silicon device measured at five temperatures ranging from 113 to 300 K is shown to be proportional to the absolute temperature. This proves experimentally the thermal origin of noise for SCLC in solids.

This paper is concerned with the detection of a random signal in white Gaussian noise when both the signal and the noise are two-dimensional random fields. The principal result is the derivation of a recursive formula for the likelihood ratio relating it to certain conditional moments of the signal. It is also shown that, except for some relatively uninteresting cases, a simple exponential formula for the likelihood ratio, such as one has in one dimension, is not possible.

Three groups of four pigeons, trained to press a treadle on a free-operant avoidance schedule, were given auditory discrimination training. Alternating 2-min components of avoidance and no shock were paired with either a tone or white noise. The pigeons were subsequently given two types of generalization tests, with and without avoidable shocks scheduled. Two of the groups, trained interdimensionally, produced excitatory and inhibitory generalization gradients along the tone frequency dimension. A predicted post-discrimination gradient was computed from the algebraic summation of these gradients of excitation and inhibition. The predicted gradient was compared with the actual post-discrimination gradient obtained from the third group of pigeons that had been given intradimensional discrimination training on the tone frequency dimension. The predicted postdiscrimination gradient agreed in shape with the empirical postdiscrimination gradient. The results in general support Spence's (1937) gradient interaction theory.

By spacing 10 stimuli (white noise) between 40 and 110 dB according to two criteria [equal response ambiguity (ERA) and equal discriminability (ED)], an attempt was made to construct an “ideal” case for magnitude estimation and category rating. The “ideal” case is defined by linear and constant Weber functions (SDs as a function of scale values) for the two scales, respectively. Altogether, three group and two individual magnitude and category rating experiments were run with these two spacings. It was found that the ERA spacing approximated the ideal case well for both Weber functions and the ED spacing only for the Weber function of the category scale. The general psychophysical differential equation that relates scale values and Weber functions for the two scales allowed good prediction of the category scales from the magnitude scales and the Weber functions. The data suggested a distinction between phenotypic (empirical) and genotypic Weber functions, analogous to “real” and “ideal” cases in physics.

A statistically efficient and computationally economical two-stage least squares procedure for the estimation of the natural frequencies and damping parameters of structural systems under stationary random vibration conditions is considered. The structural system is represented by the system of ordinary differential equations that is characteristic of lumped mass-spring-damper systems with a random forcing function. Emphasis is placed on the problem corresponding to the observation of the top story vibrations of a tall building under random wind excitation. In that case, the random excitation can be approximated by a white noise and the regularly sampled vibration record can be represented as a mixed autoregressive-moving average (ARMA) time series. The ARMA time series parameters are estimated by a two-stage least squares method using only the covariance function of the top story vibrations. The natural frequency and damping parameters of the structural system can be expressed in terms of the AR parameters. Estimates of the coefficient of variation of the structural system parameter estimates are expressed in terms of the ARMA parameter estimates. The numerical results of the least squares and maximum likelihood parameter estimation procedures worked on a real vibration data example are shown.

This paper treats the problem of minimizing the roundoff noise in digital filters using fixed-point arithmetic under sinusoidal input. A basic assumption made is that of representing the roundoff error as white noise that is independent from sample to sample and from source to source. The minimax noise principle is introduced to serve as a guide in the filter design to optimize the structure for minimum noise. One application is illustrated through the design of low-noise cascade digital filters under dynamic range constraints. Numerical examples demonstrate the lower noise possible in comparison to other known designs and serve to verify the effectiveness of a design procedure based on the minimax concept.

The response of a one dimensional isothermal atmosphere with rigid lower boundary and bounded upward by a very hot isothermal atmosphere to an applied random source is studied. It is shown that a concentrated white noise source merely excites the damped eigen-modes of the model and that the enhanced response at the cut-off frequency found in semi-infinite isothermal model is removed by the reflections. We believe that this rules out the attempts to relate the photospheric and chromospheric oscillations to the singular response of an excited semi-infinite isothermal atmosphere.

Using the concepts developed in [1] we investigate, in the presence of certain restrictions, the stability of a weakly inhomogeneous state parametrically perturbed by a small random addition of white noise. We show that when the characteristic wavelength is arbitrarily small as compared with the distance over which it varies substantially, then the mechanism of formation of the eigenfunctions responsible for the stability of the state is analogous to the mechanism given in [1]. In the present case it is not the boundaries that act as reflectors, as in [1], but the points at which the condition of existence of the global eigenfunction for the homogeneous problem holds. We obtain the criterion of stability of the state in question and discuss the problem of application of the results obtained to the case in which the ratio of the characteristic wavelength to the distance over which it varies substantially, cannot be taken as arbitrarily small.

At each level tested, the observers had to find the cut-off frequencies at which the tonal character of a white noise was beginning to change, by using a low-pass filter in one part of the experiments, and a high-pass filter in another part. The filter bandwidth which is necessary to keep unaltered the perception of the tonal character of a white noise decreases with the level of the noise; the curves obtained differ, however, from the threshold curves

A Markov analysis revealed the existence of 1st order intertrial dependence in error and response sequences from both detection and recognition tasks. Both feedback and the introduction of a burst of white noise between trials reduced intertrial dependencies in the error sequences. Task difficulty and intertrial periods affected intertrial dependence in the response sequence.

The effects of continuous white noise on the somatosensory evoked response of normal newborn infants was examined both in non-REM and REM sleep. White noise enhanced the amplitude and increased the latency of the late components of the SER in both sleep states. The results are discussed in terms of the interaction between the continuous monotonous stimulus and a discrete repetitive stimulus, as well as in terms of the sleep inducing effects of monotonous stimulation.

The effect of white noise on attention-task performance was examined as a function of the manifest-anxiety level of 30 male undergraduates with concurrent physiological recordings made. Noise interacted with manifest anxiety on two of the four attention tasks such that Ss low in anxiety improved with noise while moderately anxious Ss deteriorated with noise and highly anxious Ss remained the same. Noise had no lasting effect on heart race, skin potential, or attentional performance in general, leading to the conclusion that noise may function either as a distractor or as a behavioral arouser. Some support was gained for the inverted-U hypothesis relating arousal to performance.

An approximate analytical method is developed for predicting the stationary rms levels of response of a yielding oscillator subjected to white noise random excitation. The method is based on a power balance between the exciting force and the energy dissipating elements. Certain average period or frequency assumptions made in earlier power balance analyses have been modified to make the method significantly more accurate. The results of the analytical method have been compared with empirical data for moderately nonlinear and nearly elasto-plastic bilinear hysteretic systems (slope ratios of 1/2, 1/10, and 1/21). The empirical data include new results from a digital simulation as well as previously published analog computer results. The results of the modified power balance method are shown to agree quite well with the empirical data, particularly when the system contains little or no viscous damping. The new method is considerably more accurate than the Krylov-Bogoliubov method for nearly elasto-plastic systems.

The deafening effect of high intensity noise is well known—from rock music, aircraft, snowmobiles, motorcycles and the shooting of guns. The effects of hospital noise and its interaction with ototoxic drugs are less well known. The subject is of particular importance to pediatricians, because infants in incubators are exposed to substantial noise from the motor, airflow, respirators, slamming of incubator doors and the baby's own crying. Furthermore, animal experimentation1 shows that the ototoxic drug, kanamycin (often given to the premature infant to combat sepsis), can potentiate the effect of noise on hearing loss as much as 100-fold. Whether or not an interaction between noise and potentially ototoxic drugs occurs in man is as yet unknown. MEASUREMENT Noise has frequency and intensity. Frequency is measured in cycles per second, designated hertz (Hz). The young human ear is sensitive to a frequency range of 20 to 20,000 Hz. White noise, the auditory counterpart of white light, has equal energy in each frequency in the audible range. Intensity is measured in decibels on a scale which is linear with respect to audible frequencies. This measurement is designated dB (linear). Since the human ear is more sensitive to the damaging effects of high frequency sound than to low frequency, a better correlate with noise-induced hearing loss can be obtained when low frequencies are filtered out. Filtered sound level, measured on a so-called A-weighted scale, is designated dB(A). Room conversation produces 60 to 70 dB(A), rock music 100 to 120 dB(A) and snowmobiles 105 to 135 dB(A) for the driver.

In this paper we study the problem of designing a closed-loop system containing a constrained linear minimum-phase plant, preceded by a non-linear element whose describing function is known. The system is to be designed such that its frequency response |T(jw)| lies within specified boundaries, over the range of plant parameter uncertainty, and over a specified sinusoidal command input amplitude r max ≥ r ≥ r min-Subject to the above, the design should be such as to minimize the effect of sensor white noise at the input to the plant.

A study is presented on the digital coding of speech by means of a straightforward approximation of the time waveform. In particular, the closely related discrete-time discrete-amplitude signal representations that are rather well known as pulse-code modulation (PCM), differential pulse-code modulation (DPCM), and delta modulation (DM) are discussed. Speech is recognized as a nonstationary signal, and emphasis is therefore placed on "companding" and "adaptive" strategies for waveform quantization and prediction. With signal-to-quantization-error ratio SNR as a performance measure, techniques are suggested which are most likely to be appropriate for given specifications of information rate. It is pointed out that error waveforms in speech quantization cannot be regarded as additive white noise, in general. This means that for finer assessments of speech coders, either relative or absolute, one needs to supplement SNR-based observations with corrections for subjective and perceptual factors. The latter seem to defy quantification as a rule. Invaluable, therefore, are explicit preference tests for direct comparisons of coders from a perceptual standpoint, and notions such as isopreference and multidimensional scaling are naturally appropriate in interpreting the results of such tests. Final points of concern are communication questions such as multiple encodings of speech by tandem coder-decoder pairs; conversions among different digital code formats; and the effects of additive and multiplicative noise in the communication channel, as manifest in the erroneous reception of speech-carrying bits. Information on these topics tends to be heterogeneous and nontheoretical, and the present digression into the subject is cursory by intent. The gramophone record accompanying this paper demonstrates some of the manipulations of speech that are discussed.

Novel demodulator structures are derived using a theory for the quasi-optimal on-line demodulation of pulse-frequency modulated (PFM) signals in the presence of white Gaussian channel noise. The basic demodulator consists of a phase-locked loop with time-varying gain elements. Furthermore, its integrators are appropriately reset as each new pulse is received. This modulator may be augmented with additional integrators and gain elements to achieve quasi-optimal demodulation with delay. The quasi-optimal demodulation approaches optimal demodulation, in the minimum mean-square-error sense, as the signal-to-noise ratio increases. The various quasi-optimal receivers are derived by application of the extended Kalman filter theory to a state-space signal model.

Five experiments were conducted with normal listeners to investigate the reliability (stability) and validity (accuracy) of adaptive tests for measuring the linear portion of CNC discrimination functions. Monosyllables (consonant‐vowel‐consonant form) included in Northwestern University Auditory Test No. 6 were employed as test stimuli. Constant‐level tests were used as criterion measures to judge the accuracy of best‐of‐five (100 words), best‐of‐three (50 words), doublet (50 words), and simple‐up‐and‐down (50 words) adaptive tests. All tests were conducted under monaural (earphone) listening conditions in quiet or against a background of either 60‐ or 80‐dB‐SPL white noise. The shorter doublet tests were found to be as stable and accurate as the longer best‐of‐five procedures when seeking levels required for approximately 30% and 70% CNC discrimination. Adaptive tests using 50 words appear to be highly reliable and valid for determining the location and slope of CNC articulation functions with normal listeners.

A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformationfrom the probability density function of the random phase difference.

A feedback control policy is formulated for minimization of the expected length of time required for the state of a stochastic dynamic system to first reach a desired terminal region. The control variables are constrained and it is assumed that noise-free observations of the system state are available at all times. Dynamic programming leads to a non-linear partial differential equation that is very difficult to solve. Instead the difference between the stochastic and the more tractable deterministic equations for the switching hyperplane is represented by a truncated power series, and the optimal switching hyperplane for a ‘ bang-bang ’ controller is then computed through a search on the power series coefficients using repetitive simulations. Numerical results for the location of the stochastic switching curves for a specific second-order system with additive gaussian white noise are presented and discussed.

An equivalent noise conductivity Λn for aqueous uni-univalent electrolytes is defined on the basis of the Langevin equation. Apparatus for the recording of noise spectra and their evaluation by means of correlation methods are described. It is shown that Λn of NaCl and of KCl solutions parallels that obtained by conventional bridge methods though no external electric field as applied in the case of noise measurements. Λn for both these electrolytes is shown to obey the Debye—Hueckel—Onsager limiting law in its concentration dependence and to exhibit the usual Arrhenius form of temperature dependence. The activation energy obtained is close to that obtained from conventional bridge methods applying an external field, and closely approximates that of the viscosity of the solvent, viz. water. The noise generated by the electrolyte is shown to be white noise, being independent of frequency without any 1/f frequency component being present. There is no contact noise.

A method is described for the objective determination of the noise level in Doppler spectra. The method makes use of the physical properties of white noise and is suitable for automatic computation. It is shown that the method produces reliable results when used in conjunction with the lower-bound method of estimating vertical air velocities.

For a given nonstationary matrix covariance with a finite-dimensionality property that is the time-varying generalization of the rational power spectrum matrix property, we show how to find a linear finite-dimensional system driven by white noise with output covariance equal to the prescribed covariance.

The resolving power of a seismic array is defined in terms of the array response function and via the classical uncertainty principle. Using the theory of maximum likelihood wavenumber spectra (Capon, 1969), we show for the case of two correlated plane waves that arbitrarily high resolution is achievable in the limit as the background white noise tends to zero. This extends Barnard’s (1969) result to the case of correlated plane waves. The increased resolution arises from the additional assumption that the data are plane waves over all space, and not zero off the array as the classical result assumes. It is found that a sample rate (in time) large compared to the Nyquist rate, is needed in the case of a short time gate at a small array. Cross‐power spectral matrices are estimated at 4 hz from 1 sec of computer generated data consisting of two correlated plane waves in white noise. These spectral matrices are then used to generate maximum likelihood wavenumber spectra. The two plane waves are resolved at various signal‐to‐noise ratios and at correlations up to ρ=0.8. The need for using a high sampling rate is demonstrated. Results are compared with conventional wavenumber spectra, where the classical resolution results hold. The use of a 1‐sec window provides improved resolution of the wavenumber structure as it changes in time, resulting in better separation of any time‐overlapping phases and multipathed waves that arise from one event.

The acoustic stapedius reflex depends not only on stimulus intensity, but also on stimulus frequency, as far as reflex threshold, amplitude of response and reflex decay are concerned. The stapedius reflex threshold (SRT) for wide-band noise has been proved lower than that for pure tones. Our own investigations dealt with the relation between the SRTs for pure tones, white noise, and a 24-tone mixture (one single tone at every critical band width) in normal-hearing persons and patients suffering from sensorineural hearing lossIn normal hearing, the SRT for pure tones was measures at 70-85 dB (73-105 dB SPL) above the normal-hearing threshold in a free sound-field, the SRT for white noise (average) at 46.5 dB (68.5 dB SPL) and the SRT for the 24-tone mixture at 47.0 dB (67.2 dB SPL). In 125 patients (223 ears), the difference level between the mean SRT for tones of 0.5-4 kHz and the SRT for white noise (dl 2) was correlated with the difference level between the mean SRT for tones of 0.5-4 kHz and the mean h...

A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing (r, ?) at uniform sampling intervals T seconds apart. This development explicitly considers the coupling between the quantities measured by the sensor (r, ?) and the Cartesian x, y coordinate system selected for the tracking operation. The steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions. These results are verified by computer calculation of the Kalman filter matrix equations.

The mean square deflection of a non-linear string subjected to nonplanar Gaussian white noise excitation is determined by the perturbation method. It is shown that increase in tension due to stretching, and transverse transverse mode coupling tend to reduce the mean square deflection; while longitudinal-transverse mode coupling tends to counter this effect to some extent. These results are in conformity with the trend observed in the case of periodic excitation.

In order to avoid distorting the spectrum and introducing spurious coherency, time series shouid be filtered until they approximate white noise.2 Smith and Marcis filter interest rates by detrending with linear regression. Trend, however, is not the major problem in most economic time series. Even in the absence of trend, most economic time series contain strong positive autocorrelation and, as a result, most of the power is concentrated in the low frequencies. First differencing converts most economic time series to a reasonable approximation of white noise. Figures 1 and 2 show that detrending interest rates does not effectively eliminate the concentration of power in the low frequencies while first differencing does eliminate the concentration. Using regression techniques to remove trend also involves applying different filters to the two series, which tends to distort the phase estimates.3 In addition, from a purely practical standpoint, it generally is easier to interpret the spectrum for economic time series after the series have been converted to approximately white noise by first differencing.

A discrete receiver structure is introduced that consolidates the problems of bit detection and bit synchronization to provide optimal estimates of bit values without explicit knowledge of the transition epoch. Equations are developed for the propagation of the discrete a posteriori density function on an interval-by-interval basis. The general model is developed for a signal corrupted by additive and multiplicative noise, and the receiver structure is shown to be equivalent to a synchronous discrete receiver. The model is applied to on-off-keyed (OOK) modulation in the presence of multipath.

A class of stochastic differential equations is considered which arises by adding an additive white noise term with a small noise coefficient (2ϵ) 1 2 B and for which there exists a unique ergodic measure. An expansion in powers of ϵ of the expectations of functions with respect to the invariant measure is established. This paper was suggested by work of Fleming in which the corresponding finite time expansions were proven.

Stevens and Galanter’s (1957) iterative procedure for minimizing bias in category scaling was used for the scaling of loudness of white noise. The spacing obtained deviated systematically from a spacing constructed in accordance with an equal discriminability scale from a previous experiment (Eisler & Montgomery, 1972). For the stimulus spacing yielding a “pure” category scale, a magnitude scale was constructed too. Since the category scale could be predicted accurately by Fechnerian integration of this magnitude scale, it was concluded that the “pure” category scale is a pure discrimination scale. The discrepancy between the equal discriminability scale and the “pure” category scale was interpreted as a bias in the former scale due to greater recognizability of stimuli located at the extremes of the stimulus range.

Conditions which depend on the covariance of a vector random process, sufficient to ensure the process can be generated by a linear, invertible system of finite order driven by white noise are derived, and equations which determine the parameters of the system are found. Some structural properties of lumped covariances are given; these stress the close relation between the structure of linear systems and that of lumped covariances and provide a means of establishing the minimal order of generating systems.

An innovations approach to data compression as a viable method to improve the efficiency of data transmission is proposed. The correlated source is modeled by a ratio of polynomials with slowly time-varying coefficients. Data compression is achieved in three steps by: 1) dithering the source signal with a zero mean white noise process to enable the application of the innovations concept, 2) transforming the dithered signal to an innovations process (correlation removal), and 3) quantizing the resultant innovations process to remove unnecessary fidelity. An adaptive implementation of the data compression system using tapped-delay lines (TDL's) is obtained using the steepest descent method. Preliminary computer simulation demonstrates that, for binary data transmission, a reduction in mean square signal value of approximately 3 is attained with no observable error at a 31-dB signal-to-noise ratio (SNR).

A stationary cast-iron button sliding against a rotating cast-iron disk generated a time-varying friction signal. The signal was recorded using digital computer data-acquisition techniques. Sixty runs were taken, using different values for various parameters (such as load, velocity, and temperature). The data were analyzed on a digital computer by two different techniques. The first was a time-series analysis: the Fourier transform of each run was taken and the power spectral density of the run was studied. The second technique was a standard statistical analysis using the Kolmogorov-Smirnov goodness-of-fit test. From the two analyses, some interesting conclusions were made: 1 – the friction behaves like a random process, 2 – friction may be treated as a constant signal with superimposed white noise, 3 – the instantaneous coefficient of friction is normally distributed, 4 – friction is influenced by load and velocity, and 5 – the mean value and standard deviation are functionally related.

For a process which may not obey a stochastic linear difference equation (SDE) excited by white noise (i.e., ARMA equation), we will develop an SDE of prespecified order ( n,m ), excited by an "approximate white" noise. (The sense of approximation will be made precise in the text.) The corresponding representation is called the partially whitened representation (PWR) of order ( n,m ) for the process. A recursive method of parameter estimation is presented, and the accuracy of the estimates will be determined by analytical and simulation methods. The algorithm will asymptotically converge to the vector of coefficients of the ARMA ( n,m ) equation for the process, provided the process obeys such an equation. Otherwise, the algorithm will converge to the vector of coefficients of the PWR of order ( n,m ) for the process.

The modeling of a random process as the output of a linear, causal, and causally invertible filter has been considered by a number of authors. Various approaches that have been used are summarized here. The spectral multiplicity of the random process plays a fundamental role in this problem and permits a general and unified approach. In this framework, necessary or sufficient conditions for unit multiplicity are obtained on the system's impulse response function and on the output process itself. The role of spectral multiplicity in linear least-mean-square estimation is also clarified.

The individual noise exposure for constant sound level conditions, and hence the noise injury risk, can be estimated by conventional measurement of sound intensity, frequency and duration of exposure. The durations of different intensity components of intermittent noise of known periodicity can be easily estimated from noise index calculations such as Swedish Standard SEN 590111. For intermittent exposure where the noise source varies in an uncontrolled manner, or when the exposed person moves between different noise zones, the total exposure can be recorded by the personal noise dosimeter which instantaneously integrates sound pressure and duration of exposure.28 noise dosimeters type SRA 71 have been exposed to 100 dB “white noise” under standardized conditions. The results show good agreement between dosimeters and for the same dosimeter on different occasions. A nomogram has been prepared for converting the total noise dose to an equivalent sound level in dB(A).The Swedish norms are based on tables wh...

Predictors are derived which minimize the maximum possible mean-squared prediction error for signals observed in white noise and having a bounded kth derivative. Expressions are given for the resulting worst-case error and a suboptimal solution is presented which, for the case k = 2, performs nearly as well as the optimal and is far easier to implement.

The limiting form of the optimum stochastic regulator is determined which minimizes the steady-state expectation, Es{x′Qx + u′Ru}, for the linear process, x˙ = Ax˙ + Bu + Gv, given noisy observations y = Hx + w (with v and w being independent white noise processes) when either the control weighting matrix, R, or the spectral density matrix, W, of the observation noise, w, is singular. It is shown that as R tends from a positive-definite matrix to a non-negative definite matrix, the optimum regulator can be synthesized by a system using at most n − ks integrators, where n is the order of the system and ks equals the rank of B minus the rank of BR. Similarly, when W tends from a positive-definite matrix to a non-negative definite matrix, the optimum regulator can sometimes be synthesized by a system using at most n − rs integrators, where rs equals the rank of H minus the rank of WH. The structure of the regulator is given for each of these cases.

High school students tapped rapidly on a telegraph key to reduce the intensity of a continuous acoustic stimulus presented through earphones. Failure to respond resulted in an intensity increase of 1 dB every 4 sec. In Experiment 1, a group of 19 students responded to three pure tones (125, 1,000, and 8,000 Hz) and a white noise. The different asymptotic levels observed after 4 min were taken as a measure of equal aversion levels for the stimuli. In Experiment 2, the effect of the starting intensity level (45, 70, and 90 dB SPL) was determined for a 1,000-Hz tone. Differences in the asymptotic intensity levels observed after 6 rain were not significant. In Experiment 3, no significant effect was found upon varying the number of responses required to produce a 1-dB intensity decrement in a 1,000-Hz tone. Together, the experiments demonstrated the feasibility of determining equal-aversion levels for sounds.