Average Noise Power Research Articles

Electrochemical Noise Generation during SCC of a High-Strength Carbon Steel

Abstract Stress-corrosion cracking experiments have been performed on a high-strength carbon steel exposed to acidified sodium chloride solution poisoned with sodium sulfide. The electrochemical potential of the specimen was monitored during the experiment, and this paper reports the observed electrochemical noise. The analysis was performed using both the maximum entropy method and the discrete Fourier transform. A consistent noise behavior was observed throughout the experiment, with the only perturbation of any significance being associated with major transients that occurred when the specimen actually failed. The average noise power measured over a period of the same order as the duration of the transients has been found to be an effective method of detecting them, but it is expected that this will be much more difficult in service conditions.

Detection threshold calculations for Weibull interference

The Weibull probability density function (pdf) has been used to represent the noise-only output of an envelope detected matched filter when the input noise contains non-Gaussian, high amplitude components. This situation may occur in active sonar when the total interference is dominated by reverberation. The familiar Rayleigh pdf associated with Gaussian input noise is a member of the Weibull family with a shape factor of 2. If the threshold for detection is based on an assumed Rayleigh density and the noise changes to Weibull with a shape factor less than 2, the false alarm rate will increase dramatically even if the average noise power is unchanged. Therefore, in order to maintain a constant false alarm rate (CFAR), the threshold must be raised. This will result in an increase in the signal to noise ratio required to achieve a specific probability of detection (Pd). It is necessary to determine the signal plus noise pdf to quantitatively evaluate this effect on detectability. An integral formulation of this function has been derived by Eckstrom, and it has been numerically integrated for a few cases by Nilsson and Glisson. The present authors have developed a much simpler approximate procedure for computing receiver operating characteristic (ROC) curves for a linear detector in Weibull noise that does not require numerical integration. This method is based on the premise that the signal plus noise pdf is not strongly affected by the Weibull shape parameter, at least over the 10% < Pd < 90% range. In this paper, the details of this approximate technique are presented, and some comparisons with more exact calculations are provided.

In situ acoustic calibration for a large aperture array

During September 1987, a large aperture acoustic array was deployed vertically in the Northeast Pacific to study low-frequency noise in the ocean. Coherent combination of the 120-channel outputs requires knowledge of individual element amplitude and phase response for accurate results. Two in situ methods of array calibration are described and results from the September experiment are presented. The first method used transmissions from a low-frequency source of known location and power level. Simulating the conditions encountered during the transmission, the power arriving at the array was predicted by several acoustic propagation models. By comparing the array response at specific frequencies to the response predicted by the models, an absolute calibration was obtained. An error curve for the phase data was generated by unwrapping the phase, accounting for a sampling offset in the array, and subtracting a multiple linear regression curve. The second method determines relative amplitude levels by examining the average ambient noise power output of a specified frequency band across the array. Using spectral, coherence, and directionality plots, the level of self-noise in the array was shown to be below that of the ambient noise being measured. These two independent methods provide a consistent set of element calibration values used for array beamforming. [Work supported by ONT.]

The practical significance of two-dimensional deconvolution in echography

This paper evaluates deconvolution (inverse filtering) as applied to ultrasonic imaging systems, and discusses the obstacles which are encountered employing the technique in practice. A minicomputer is used to generate artifical echo signals, simulating rf signals resulting from a set of point reflectors in a homogeneous medium, as recorded by an electronically focused group-steered linear array scanner. Two-dimensional deconvolution in combination with a Wiener noise reduction filter (i.e., a Wiener-Inverse filter) is applied to these simulated rf signals, which were contaminated with white noise. The efficacy of the Wiener-Inverse filter is defined in terms of its ability to resolve two point reflectors with a lateral spacing equal to the local −6 dB width of the ultrasonic beam. In favorable circumstances, the targets are resolved at signal-to-noise ratios (SNR) better than 20 dB, where SNR is defined as the maximum signal power divided by the average noise power level. Nonlinear effects due to quantization or signal clipping are investigated. In order to improve the resolution of an rf signal with a dynamic range of 40 dB, the input signal should be digitized at a minimum of 12 bits. The problem of signal clipping can be circumvented by oversampling. The two-dimensional Wiener-Inverse filter is defined in terms of both temporal and spatial properties of the insonification. Effects of wave diffraction give rise to a depth-dependent ultrasonic beam. As a result of a misfit of the Wiener-Inverse filter and the local properties of the ultrasonic beam, erroneous noisy texture arises in the image. Adaptation of the Wiener-Inverse filter with respect to the beam properties gives acceptable results, at the expense of a rather large computational effort.

The practical significance of two-dimensional deconvolution in echography.

This paper evaluates deconvolution (inverse filtering) as applied to ultrasonic imaging systems, and discusses the obstacles which are encountered employing the technique in practice. A minicomputer is used to generate artificial echo signals, simulating rf signals resulting from a set of point reflectors in a homogeneous medium, as recorded by an electronically focused group-steered linear array scanner. Two-dimensional deconvolution in combination with a Wiener noise reduction filter (i.e., a Wiener-Inverse filter) is applied to these simulated rf signals, which were contaminated with white noise. The efficacy of the Wiener-Inverse filter is defined in terms of its ability to resolve two point reflectors with a lateral spacing equal to the local -6 dB width of the ultrasonic beam. In favorable circumstances, the targets are resolved at signal-to-noise ratios (SNR) better than 20 dB, where SNR is defined as the maximum signal power divided by the average noise power level. Nonlinear effects due to quantization or signal clipping are investigated. In order to improve the resolution of an rf signal with a dynamic range of 40 dB, the input signal should be digitized at a minimum of 12 bits. The problem of signal clipping can be circumvented by oversampling. The two-dimensional Wiener-Inverse filter is defined in terms of both temporal and spatial properties of the insonification. Effects of wave diffraction give rise to a depth-dependent ultrasonic beam. As a result of a misfit of the Wiener-Inverse filter and the local properties of the ultrasonic beam, erroneous noisy texture arises in the image. Adaptation of the Wiener-Inverse filter with respect to the beam properties gives acceptable results, at the expense of a rather large computational effort.

Analysis of polarization fluctuation in single-mode optical fibers with continuous random coupling

A new analysis method is developed to study the polarization fluctuation in conventional single-mode optical fibers. A random partial differential equation is derived to describe the continuous random coupling between two eigenpolarization modes caused by the perturbation of permittivity along fibers. The calculation formulas for the polarization fluctuation are given. By these formulas, it is proved that the average noise power of the fluctuation at the fiber output depends on the fiber length, the correlation length of perturbation, and the variance of disturbances.

Measurement and statistical analysis of wideband MF atmospheric radio noise: 2. Impact of data on bandwidth and system performance

Measurements of wideband medium frequency atmospheric noise have been made over the past several years in the southwestern United States. In part 1 of a two‐part paper the measurement and data transcription system and the statistical analysis software used to analyze the data are presented. Specific results given in part 1 include the temporal structure of the noise and the distribution and time variation of the measured average noise power. In part 2, representative first‐ and higher‐order statistics and the impact of the data on bandwidth and system performance are described. Specifically, bit error rate simulations of a coherent receiver operating in either modeled or measured atmospheric noise are presented.

Measurement and statistical analysis of wideband MF atmospheric radio noise: 1. Structure and distribution and time variation of noise power

Wideband measurements (100 kHz) of medium frequency atmospheric noise have been made over the past several years in the southwestern United States. In part 1 of a two‐part paper the measurement and data transcription system and the statistical analysis software used to analyze the data are presented. In part 2, representative first‐ and higher‐order statistics and the impact of the data on bandwidth and system performance are described. Measurement results presented in part 1 include the temporal structure of atmospheric noise, the distribution and time variation of the measured average noise power, and comparisons with predictions by the International Radio Consultative Committee (CCIR).

VHF Radio Noise Measurements Near a Roadway Carrying 10 000 Vehicles per Hour

Measurements of noise power spectral density were recorded with a vertical monopole at 47 MHZ, about 0.5 km from Interstate Highway I-95 (Massachusetts Route 128), in Waltham, Massachusetts, which was carrying traffic approaching 10 000 vehicles per hour. Average noise power values were found to be in excellent agreement with predictions based on vehicle density reported by Spaulding in 1972.

NAR AGC adaptive detection of signals deformed by random linear filtering using generalized matched and antimatched filters

The adaptive detection of signals deformed by random linear filtering in noise with fluctuating power is considered. An automatic gain control (AGC) receiver comprising both generalized matched and antimatched filters is proposed. The antimatched filter is inserted in the AGC channel in order to minimize the average power signal-to-noise ratio, and thus renders the AGC approximately insensitive (transparent) to strong signals, which is the property of a noise alone reference (NAR). On the other hand, the generalized matched filter is used to maximize the ratio of the average received signal power to the average noise power which has been regulated by the AGC. Computer simulation results show cearly the good performance of the proposed AGC receiver.

Least squares quantization in PCM

It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2^{b}</tex> quanta, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b=1,2, \cdots, 7</tex> , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.

Integrating acousto-optic channelized receivers

The subject of this paper is acousto-optic channelized receivers with large noncoherent processing gain. A receiver model is developed and the output statistics are derived for signal plus noise input. Noise equivalent bandwidths and signal detection sensitivity are calculated. The implications of large average noise power are discussed. Experimental measurements are in agreement with the theory presented.

The average noise from a Poisson stream of vehicles

The distribution of the average noise power from a Poisson stream of vehicles is, properly normalised, shown to converge to a normal distribution although the corresponding stationary process is deterministic. The speed of convergence is estimated. Finally the asymptotic efficiency of a sampling procedure is discussed.

The average noise from a Poisson stream of vehicles

The distribution of the average noise power from a Poisson stream of vehicles is, properly normalised, shown to converge to a normal distribution although the corresponding stationary process is deterministic. The speed of convergence is estimated. Finally the asymptotic efficiency of a sampling procedure is discussed.

Seismic noise survey in Long Valley, California

In June 1973, seismic noise measurements were made in Long Valley, California, as part of the U.S. Geological Survey's geothermal investigations. Spatial variation of the average noise power shows high levels of noise extending over most of the eastern half of the Long Valley caldera. Since the noise high is almost similar in extent to the soft sedimentary Owens River basin, it is possible that ground amplification of seismic waves is at least partially responsible for the noise anomaly. Two lines of evidence indicate that geothermal noise may be present in Long Valley. (1) Relative amplification of teleseismic waves over soft ground, with respect to a reference station on hard rock, is about 12 dB. The noise anomaly, however, is at least 12 dB higher than this value. It is therefore difficult to explain the anomaly by postulating ground amplification of regional noise, thus indicating that a noise source may be present in the area of the anomaly. At wave frequencies below 2 Hz, river and cattle noise do not contribute much to the anomaly. (2) Group velocities of seismic noise, measured by using arrays, are in general quite low except at a few stations along the southern edge of the noise anomaly. The wave azimuths in the low-velocity areas show random propagation, whereas azimuths associated with the high-velocity waves point to the area where surface geothermal phenomena are found. The high-velocity waves also have frequencies below 2 Hz. If a noise source is present under the southern edge of the sedimentary basin, it could excite the basin much more than it does the hard ground directly above it and thus produce the observed noise anomaly.

Measurements of amplitude probability distributions and power of automobile ignition noise at HF

Measurements of the amplitude probability distribution (APD) of the envelope and measurements of other parameters of automobile ignition noise were made at frequencies between 24 and 30 MHz. The measurements were conducted at a quiet site where several single stationary vehicles were operated at engine speeds corresponding to idle and cruise. Measurements were also made at two distances near a freeway, for light traffic (approximately 20 vehicles per min) and for heavy traffic (approximately 45 vehicles per min). The principal instrumentation consisted of several phase-stable receivers with coherent quadrature detectors whose outputs were digitized at a rate of 200 samples per quadrature component per second and recorded on magnetic tape for computer processing. About 10 min of data (about 120 000 samples) were obtained during each measurement. The computer plotted the APD on a Rayleigh scale in dB relative to thermal noise and calculated the mean noise power available at the antenna terminals (related by a constant to the noise factor F <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</inf> ) and V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> --the ratio in dB of rms to average voltage. The average power of the ignition noise increases with engine r/min and V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> usually decreases. Near a freeway, most of the noise is contributed by a small number of very noisy vehicles. The APD's for various situations are strikingly similar; all show that most of the noise envelope samples in a measurement are Rayleigh distributed. A small percentage of the noise samples do not follow the Rayleigh distribution, but are of higher amplitude. This percentage is higher for an engine at cruise speed than at idle speed, and higher for heavy traffic than for light traffic.

Exact Evaluation of Delta Modulator Performance in Sonar Signal Processors

Single-bit delta modulation is increasingly being used or suggested for telemetry and beam-forming in sonar receiving systems. To evaluate its performance in these applications, an exact time-domain analysis appropriate for logic circuits practically used was formulated, which served as the basis for the development of a computer program for the simulation of the codec (coder-decoder). The essence of this formulation lies in a more rigorous calculation of the local decoder output voltage corresponding to an arbitrary coder output bit pattern in terms of the pole locations of the integrating network. The difference between the local decoder output and the analog input signal represents the quantization noise. Utilizing an 800-Hz sinusoidal signal as the analog input to the codec, local decoder output waveforms for a number of cases were calculated and displayed to show the decrease of quantization noise with increasing clock frequency and the improvement of codec performance with double integrating network. The average quantization noise power was also calculated from samples of noise waveform to illustrate the quantitative determination of the output SNR and the dynamic range of the codec. Further work directed specifically at sonar beamforming applications is being planned.

The Effect of Spectral Shape on the Probability of Error in Laser Binary Communication Systems

The effect of spectral bandwidth and spectral shape upon laser binary communication systems is investigated. The probability of error is plotted as a function of bandwidth for Lorentzian and Gaussian shaped spectra. The results show that even when the average noise power and the signal-to-noise ratio are held constant, the probability of error varies considerably as a function of spectral bandwidth.

An Analysis of Metropolitan Incidental Radio Noise Data

Multiple sets of incidental man-made radio noise data assembled from many sources are examined to determine their variation with frequency and distance. Separate treatments are provided for both average noise power and quasipeak noise field intensity data. The frequency and distance variations of average noise power are examined within the intervals 500 kHz to 1 GHz and 1 to 23 miles from an urban center. At several urban separation distances the frequency dependence of quasi-peak noise field intensity is presented for a large portion of the frequency interval between 15 kHz and 400 MHz.

Adaptive Detection Probabilities for Fluctuating Target Models in Nonhomogeneous Gaussian Noise

Under the assumption that the average noise power may vary from cell to cell, new, more easily computed expressions are given for the probability of detecting a fluctuating target by means of a cell-averaging CFAR test. The generalized chi-square family of fluctuating targets is considered with the Swerling I and III models given as special cases.