Probability Density Function Of Signal Research Articles

Frequency-domain blind deconvolution based on mutual information rate

In this paper, a new blind single-input single-output (SISO) deconvolution method based on the minimization of the mutual information rate of the deconvolved output is proposed. The method works in the frequency domain and requires estimation of the signal probability density function. Thus, the algorithm uses higher order statistics (except for Gaussian source) and allows non-minimum-phase filter estimation. In practice, the criterion contains a regularization term for limiting noise amplification as in Wiener filtering. The score function estimation, which represents a key point of the algorithm, is detailed, and the most robust estimate is selected. Finally, experiments point to the relevance of the proposed algorithm: 1) any filter, minimum phase or not, can be estimated and 2) on actual data (underwater explosions, seismovolcanic phenomena), this deconvolution algorithm provides good results with a better tradeoff between deconvolution quality and noise amplification than existing methods.

A simplified model of gas–liquid two‐phase flow pattern transition

AbstractAn experiment of upward gas–liquid two‐phase flow was conducted in an air–water isothermal system under atmospheric pressure. The differential pressure was measured at the fully developed section by using a variable reluctance type transducer to classify the flow patterns and their transitions. The flow behavior was observed with a high‐speed video camera. The probability density function (PDF) of the differential pressure signal was employed to identify the flow pattern. A simplified one‐dimensional flow model was proposed to clarify dominant factors affecting the formation and transitions of flow patterns. The model dealt with the gas‐component advection based on the spatiotemporal void fraction behaviors by considering the gas compressibility, the wake, and the liquid phase redistribution mechanism. The simulation results of the model indicated four kinds of the void wave patterns (ripple‐like, rectangular, distorted rectangular, and uniform wave patterns) depending on gas and liquid volumetric fluxes. These void wave patterns corresponded well to the experimentally observed flow patterns. The transitions among void wave patterns agree well with the Mishima–Ishii flow pattern map. The friction loss estimated by the present model coincides fairly well with Chisholm's empirical formula. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 445–461, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20029

Performance of laser tracking of small targets during turbulence and beam jitter

Small target detection and tracking are important for laser radars in many applications such as laser weapons, directed infrared countermeasures (DIRCM), fire control, target recognition, and free-space laser communications. The detection and tracking performance depends on the mode of detection, SNR, target signal statistics, beam jitter, and turbulence induced irradiance variations. We show results of the root mean square (rms) tracking error versus SNR primarily for direct detection systems using a strong glint return. For the general case of a certain signal and noise probability density functions (pdf) it is hard to obtain analytical solutions for the mean and variances of the estimates for the rms tracking error. We have therefore used numerical simulations to illustrate how the pdf and SNR will affect the tracking accuracy. Gamma functions and other pdf's can be used to characterize the signal distributions to get a first hand on tracking performance. The results are presented as tracking errors versus the angular spot size of the laser beam in the tracking detector plane. We also investigate the beam optimization problem for target detection and "power in bucket," which is maximizing the laser energy at the target. We find that there are optimum beam sizes (w) versus the rms jitter () and that optimum w/ (minimizing the false alarm rate for a given detection probability Pd) typically fall in regions 1 to 3 depending on probability of detection and the representative pdf for the application in mind.

Microscopy of localized second-harmonic enhancement in random metal nanostructures

Using second-harmonic (SH) scanning optical microscopy in reflection we study the effect of localized SH enhancement in random metal nanostructures. With a tightly focused tunable (750--830 nm) laser beam, we obtain SH images of a 55-nm-thick gold film surface covered with randomly distributed 70-nm-high gold bumps showing small $(\ensuremath{\sim}0.7\ensuremath{\mu}\mathrm{m})$ and very bright $(\ensuremath{\sim}{10}^{3}$ times the background) spots. Wavelength and polarization dependencies of both positions and intensities of these SH bright spots as well as their statistics are investigated and compared for two areas having different nominal densities of scatterers, i.e., 25 and $50\ensuremath{\mu}{\mathrm{m}}^{\ensuremath{-}2}.$ For relatively large signals, it is found that, the probability density function of the SH signal follows the power-law dependence with the index being in the range of 2.5--3 for both values of the scattering density. We observe that, for incident laser powers in the range 3--40 mW, the SH bright spots exhibit, as expected, quadratic dependencies of the maximum signal on the incident power. However, for higher power levels, the interrogating laser beam causes nonlocal modifications of SH images, i.e., some SH bright spots disappear and others emerge even outside of the area that was exposed to a high power radiation. We relate the observed feature to surface plasmon polariton contribution in the process of multiple scattering, resulting in the formation of resonant eigenmodes (at fundamental and SH frequency) whose excitation in turn gives rise to the SH bright spots.

Measurement of Void Fraction and Pressure Drop of Air-Oil Two-Phase Flow in Horizontal Pipes

The void fractions, flow regimes, and pressure drop of air-oil two-phase flow in a half-inch diameter pipe over a wide range of test conditions have been investigated. The flow regimes were identified with the aid of a 1000 frames per second high-speed camera. A capacitance sensor for instantaneous void fraction measurements was developed. The mean and probability density function of the instantaneous void fraction signal can be used to effectively identify the different flow regimes. The current flow regime data show significant differences in the transitional boundaries of the existing flow regime maps. Property correction factors for the flow regime maps are recommended. The pressure drop measurements were compared to the predictions from four existing two-phase flow pressure drop models. Though some of the models performed better for certain flow regimes, none of the models were found to give accurate results over the entire range of flow regimes.

A Simplified Model of Gas-Liquid Two-Phase Flow Pattern Transition.

An experiment of upward gas–liquid two-phase flow was conducted in an air–water isothermal system under atmospheric pressure. The differential pressure was measured at the fully developed section by using a variable reluctance type transducer to classify the flow patterns and their transitions. The flow behavior was observed with a high-speed video camera. The probability density function (PDF) of the differential pressure signal was employed to identify the flow pattern. A simplified one-dimensional flow model was proposed to clarify dominant factors affecting the formation and transitions of flow patterns. The model dealt with the gas-component advection based on the spatiotemporal void fraction behaviors by considering the gas compressibility, the wake, and the liquid phase redistribution mechanism. The simulation results of the model indicated four kinds of the void wave patterns (ripple-like, rectangular, distorted rectangular, and uniform wave patterns) depending on gas and liquid volumetric fluxes. These void wave patterns corresponded well to the experimentally observed flow patterns. The transitions among void wave patterns agree well with the Mishima–Ishii flow pattern map. The friction loss estimated by the present model coincides fairly well with Chisholm's empirical formula. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 445–461, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20029

Nonsymmetric PDF estimation by artificial neurons: Application to statistical characterization of reinforced composites

We present a generalized adaptive activation function neuron structure which learns through an information-theoretic-based principle, which is able to estimate the probability density function of incoming input. It provides a low-order smooth robust estimate of the input signal probability density function. The presented method has been developed with reference to statistical characterization of polypropylene composites reinforced with vegetal fibers, that the proposed numerical experiments pertain to.

Direct observation of localized second-harmonic enhancement in random metal nanostructures.

Second harmonic (SH) scanning optical microscopy in reflection is used to image the gold film surface covered with randomly placed scatterers. SH images obtained with a tightly focused tunable (750-830 nm) laser beam show small (approximately 0.7 microm) and very bright (approximately 10(3) times the background) spots, whose locations depend on the wavelength and polarization of light. Comparing SH and fundamental harmonic (FH) images, we conclude that the localized SH enhancement occurs due to the overlap of FH and SH eigenmodes. The probability density function of the SH signal is found to follow the power-law dependence.

Nonlinearity representation and PDF measurement of ADC testing signals

A method suitable for quantifying nonlinearities in stochastic signals, determining their trend with frequency and for assessing the adequacy of a stimulus signal in a statistical testing method will be presented in this paper. Further, both the experimental setup, which allows for the extraction of the probability density function of the stimulus signal, and the representation of the nonlinearities, will be approached. Finally, two case studies concerning the noise and the sinusoidal stimulus will be presented as well as experimental data relating the application of the method to a commercial arbitrary waveform generator (sinusoidal output).

Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems.

The average bit error rate (BER) of optical communication systems is considered in the presence of random angular jitter. First, the received power and the BER in the absence of jitter are reviewed. Then the average BER is obtained in the presence of circularly symmetric, normally distributed jitter by using the probability density function of the optical signal. By minimizing the power penalty for average BER, the optimum ratio of the divergence angle of the laser beam to the random angular jitter at the desired BER is obtained. An analytic approximation of the optimum ratio is derived as a function of the desired average BER. The results can be used for designing the link budget of optical communication and tracking channels in the presence of jitter.

Transient density signal analysis and two-phase micro-structure flow in gas–solids fluidization

A dual-optic density probe was used to investigate the transient signals of local solids fraction at different radial positions on an axial section in a 186 mm diameter (ID) gas–solids fluidized bed, which was operated under the conditions of superficial gas velocity of 0.025– 10.2 m/s with 75 μm FCC particles. The analysis of probability density function (PDF) of the density signal shows that two kinds of stable phase structures exist in bubbling, turbulent, circulating, and pneumatic transport fluidized beds. The dilute phase structure is termed “void”, characterized by a continuous gaseous phase with a log-normal solids fraction distribution. The dense structure is termed “cluster”, characterized by a continuous solids phase with a normal solids fraction distribution. The interactions between the two phases in the space scale and the time scale form the macroflow phenomena. The properties of phase structures are uniform over the cross section, and change with the operating conditions. Based on the characteristics of voids and clusters and the interactions between them, a new explanation of the mechanism of gas–solids fluidization through four regimes is proposed.

Analysis of CDMA signal spectral regrowth and waveform quality

Closed-form expressions for the spectral regrowth and waveform quality of a reverse-link code divison multiple access (CDMA) signal passed through a weakly nonlinear circuit are derived using the power series and statistical methods. The third-order nonlinearity is expressed in terms of IP/sub 3/ to include the memory effects of the circuit in-band and out-of-band reactances. The analysis is based on a time-domain model of the signal that gives more accurate distortion estimates than the widely used Gaussian approximation. The model is used to derive the probability density function and other statistical properties of the CDMA signal to compare them to the Gaussian noise properties. Differences in statistics and distortions of OQPSK and QPSK modulated signals are discussed.

Multi-tone testing of quantisers using PRBS signals

This paper compares the advantages and disadvantages of multi-tone testing with single-tone (sine-wave) testing and proposes the use of pseudo random binary sequence (PRBS) based multi-tone test signals. Single-tone testing is convenient as a pure test signal as it enables the practical performance of analogue to digital converter (ADC) to be compared with its theoretical value at one frequency and amplitude. ADCs exhibit non-linearity that depends on the rate of change and amplitude of the signal and on the amplitude probability density function (APDF) of the test signal. Tests that are sensitive to these effects will therefore assist manufacturers in improving their designs, and users in selecting the best device for their application. A test procedure that enables conventional ADC dynamic test parameters to be measured with the PRBS test signal is described.

Effects of time averaging on optical scintillation in a ground-to-satellite atmospheric propagation

Temporal natures for a variance of turbulence-induced log-intensity fluctuations are obtained. The variance of the optical fluctuation is reduced when the optical signals are integrated in a photodetector, and we express the index of reduction (called the time-averaging factor) by using an autocovariance function of the optical fluctuation. The optical fluctuations for a ground-to-satellite path are caused by both atmospheric turbulence and the beam-pointing jitter error of the optical transmitter. The turbulence-induced optical scintillation can be discriminated from the fluctuation that is due to the beam-pointing jitter error. The compared result from the probability density function of the optical signal reveals good agreement. The temporal autocovariance functions of optical scintillation are obtained and used to calculate the time-averaging factor. The analytically expected effects of time averaging are verified by the experimental results. The estimations contribute to the link budget design for the optical tracking channel through atmospheric turbulence.

Improving performance of a CdZnTe imaging array by mapping the detector with gamma rays

We can greatly reduce image artifacts in our pixellated CdZnTe arrays by mapping imperfect regions with a narrow collimated beam of gamma rays. Portions of our detectors produce signals that agree well with simulations of gamma-ray interactions, but there are many examples of structures in the material that respond unpredictably to gamma rays. We mapped some of these imperfect regions using 60 and 140 keV gamma-ray beams, recording a 7×7 set of pixel signals for each interaction. The pixel pitch was 380 μm. We used the mapped data to estimate the probability density function (PDF) of the pixel signals for each interaction position. Images were taken on the mapped sections, storing each gamma ray as a list of pixel signals. Images could be formed by either estimating each gamma-ray interaction position individually or using the entire set of image data in a single iterative computation using the expectation-maximization (EM) algorithm. At 60 keV individual interaction positions were estimated by fitting the data to a Gaussian PDF, correcting the artifacts and giving sub-pixel resolution of less than 150 μm in some regions. At 140 keV applying the EM algorithm was necessary for improving the images.

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x, y)-plane and eight in the (x, z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re θ?5000.

Estimation of probability density function using spectral analysis

The authors present a new bound on the estimation of the probability density function of random signals, using Woodward's theorem, correlation techniques and spectral analysis. The proposed method is based on the spectral analysis of the random process.

Effect of Void Fraction on Vibrational Behavior of Tubes in Tube Bundle Under Two-Phase Cross Flow

The effects of local two-phase flow parameters on the vibrational behavior of tubes have been studied in an in-line 5 × 20 tube bundle subjected to air-water cross-flow. One of the tubes was flexibly mounted and instrumented for vibration measurement and the others were rigid. Parameters obtained include local void fraction fluctuations, RMS amplitude of void fraction fluctuations, void fraction distributions across the tube bundle, flow regimes based on probability density function of void fraction signals, damping ratio, and tube vibration response as a function of mass flux, void fraction and dynamic pressure. Damping and tube vibration amplitude in two-phase flow have been found to be closely related to the RMS amplitudes of the local void fraction fluctuations and dynamic pressure fluctuations, respectively.

Algorithm for optimal filtering of random Markov signals with pulse-disturbance-amplitude estimation

Optimal filtering problem of random Markov signals with simultaneous estimation of pulse disturbance amplitudes is considered. Linear models of stochastic difference equations in discrete time are used to describe signals, observed processes, and pulse disturbances. Pulse disturbances occur at random times with random amplitudes. A real-time calculation procedure is obtained for the joint a posteriori probability density function of random signals and pulse disturbance amplitudes. A quasioptimal filtering algorithm is derived in the case of scalar signals and scalar observed processes by a partition method. Computer simulation results are presented.

Evaluation and verification of the VHF/UHF propagation channel based on a 3-D-wave propagation model

This paper is intended to increase and improve the knowledge concerning the characterization of digital VHF/UHF communication channels. This characterization of the propagation channel is based on the field strength-delay-spectrum (FDS) of the three-dimensional (3-D) multipath wave propagation. A statistical superposition of the predicted multipath signals yields the probability density function of the narrowband signal and the averaged channel impulse response of the wideband propagation channel. Thereof, the relevant parameters, e.g., standard deviations, mean values, delay spread, and correlation coefficients, are derived both in time and frequency domain. The angles-of-arrival of the multipath signals are used to calculate the Doppler spectra of moving receivers for the characterization the time-variant properties of the propagation channel. In total, a rather complete summary of derivations, algorithms and characteristics of the VHF/UHF propagation channel is presented. Narrowband and wideband measurements are included for verification.