Gaussian Amplitude Distribution Research Articles

Paraxial and ray approximations of acoustic vortex beams.

A compact analytical solution obtained in the paraxial approximation is used to investigate focused and unfocused vortex beams radiated by a source with a Gaussian amplitude distribution. Comparisons with solutions of the Helmholtz equation are conducted to determine bounds on the parameter space in which the paraxial approximation is accurate. A linear relation is obtained for the dependence of the vortex ring radius on the topological charge, characterized by its orbital number, in the far field of an unfocused beam and in the focal plane of a focused beam. For a focused beam, it is shown that as the orbital number increases, the vortex ring not only increases in radius but also moves out of the focal plane in the direction of the source. For certain parameters, it is demonstrated that with increasing orbital number, the maximum amplitude in a focused beam becomes localized along a spheroidal surface enclosing a shadow zone in the prefocal region. This field structure is described analytically by ray theory developed in the present work, showing that the spheroidal surface in the prefocal region coincides with a simple expression for the coordinates of the caustic surface formed in a focused vortex beam.

EFFICIENT INCREMENTAL SIMULATION OF “1/f” NOISES

Large-scale simulations and analysis of the original powers of 2 geometric source sum algorithm for simulating [Formula: see text] noise confirm that it provides a reasonably accurate approximation to an exact [Formula: see text] spectral density with a Gaussian amplitude distribution over any arbitrarily large frequency range. This incremental algorithm is computationally efficient with a computation time, after initialization, that varies linearly with the number of samples generated. A new variation allows non-integer and random ratios for the geometric sequence that reduces variations about the exact power-law spectral density and, by varying individual source amplitudes, produces generalized [Formula: see text] noises.

An efficient 5.8 GHz microwave wireless power transmission system

This study demonstrates an efficient 5.8 GHz microwave wireless power transmission (MWPT) system. The whole system comprises a transmitting subsystem and a receiving subsystem. A 64-way phased microwave power source and a transmitting antenna array of 1 m × 1 m are included in the transmitting subsystem. By exciting the transmitting array with a 10-dB Gaussian amplitude distribution and a quadratic phase distribution via the phased microwave power source, the transmitting subsystem radiates a low side-lobe and focused microwave beam. The receiving subsystem comprises a receiving antenna array of 0.5 m × 0.5 m and 64 rectifiers. The efficient receiving antenna array and rectifiers realize an efficient rectenna array. An experiment on the MWPT system is conducted. The total microwave power output from the source is 24 W, and the transmission distance is 10 m. According to the measurements, the total rectified direct current (DC) power is 4.58 W, and the overall RF-DC efficiency is 19.08%.

Efficient Performance Bound for Channel Estimation in Massive MIMO Receiver

In this paper, we present a new performance bound for uplink channel estimation (CE) accuracy in the Massive Multiple Input Multiple Output (MIMO) system. The proposed approach is based on noise power calculation after the CE unit in a multi-antenna receiver. We decompose a non-line of sight (NLOS) channel into separate taps and calculate the cross-covariance matrix between them. Then a linear minimum mean squared error (MMSE) method is applied with these taps to estimate residual CE error value for each unique scenario, assuming Gaussian distribution of tap amplitudes and antenna noise. An artificial CE is calculated as a sum of the ideal noiseless channel (pre-defined Quadriga model) and the leftover noise after the optimal estimate. The artificial CE is then utilized in the MIMO detector and decoder units to calculate performance bound. Our method outperforms the accuracy of a well-known Cramer-Rao lower bound (CRLB) due to considering more statistics (number of taps and correlation between them) since performance strongly depends on several channel taps and their power ratio. Additionally, we show that our bound can be obtained from the generalized Bayesian CRLB. Simulation results are presented for the 5G QuaDRiGa 2.0 NLOS channel.

Influence of edge cutting process on fatigue behaviour of spectrum loaded aluminum sheets

Car body and chassis components made of aluminum or steel sheets are produced with varying cutting processes in the different development stages. Whereas the series components are mainly manufactured by shear cutting, the prototype components are often produced with laser cutting. Each cutting process results in specific properties for the cut-edge like surface finish, hardness distribution and residual stresses in the near surface region. The fatigue crack in such components usually starts from a cut-edge, making the fatigue lifetime dependent on different cut-edge conditions. In literature the influence of the cut-edge conditions on the fatigue behaviour so far mainly focuses on constant amplitude loading. Therefore the influence of variable amplitude loading on the cut-edge effect is the objective of this paper. The results of stress-controlled fatigue tests with constant and variable amplitude loading, using a random Gaussian amplitude distribution, are compared for aluminum sheets with different cut-edge conditions. These results show an influence of the load-time-history on the cut-edge effect. The decrease of the fatigue strength under variable amplitude loading is significantly less than for constant amplitude loading. However since the Gassner-lines are shallower than the Woehler-lines the decrease of the fatigue life is higher under variable amplitude loading compared to constant amplitude loading.

Influence of circular and annular pupil function on Axial Point Spread Function of optical system

The paper presents an analysis of influence of shape and transmissivity of a pupil of an optical system on an axial energy distribution while the optical system images axial point. Therefore, a depth of focus is studied. Specifically, the analysis is done for uniform illumination of a circular pupil, and for the circular and annular pupil in the case of Gaussian amplitude distribution. Analytical formulas for Point Spread Function and Axial Point Spread Function are described, and characteristics of properties of the depth of focus of the optical system are derived. The novel analytic formulas presented in the paper can be used for determination of the value of the depth of focus of the optical system for given threshold limit of normalized axial intensity.

REFLECTION OF LIGHT FROM THE DIFFRACTION GRATING WITH TRIANGULAR PROFILE

we study the light diffraction at a reflective grating with triangular profile in scalar wave optics approximation. The case of 1D diffusively reflective rough surface can be described in the first approximation as a random set of reflective gratings with triangular profiles, which are characterised by normal (Gaussian) distribution of amplitude and spatial period. We have obtained the condition for amplitude and period of a diffraction grating in the case of absence of secondary reflections, and the dependence of optical path difference on amplitude and spatial period of the triangular profile. We have investigated the influence of triangular profile parameters on the intensity of reflected wave. We have measured the relative intensity (reflection coefficients) of rough surface reference samples in the case of normal incidence. The relative intensity of reflected wave in the case of normal incidence is used in the design of optical contactless methods for the characterisation of rough surfaces in range of 0.05…0.25 mm. We suggested an optical scheme for the surface roughness measurements, and tested it on the reference samples of rough surfaces. We investigated the dependence of reflected wave intensity on the diffraction angle, and simulated it using numerical solutions of Maxwell equation (FDTD methods). Therefore, we demonstrate that measurements of relative intensity of the reflected wave in the normal to sample plane direction in an objective focal plane allow for determination of the roughness of diffusely reflective surfaces

Positive and negative linear chirping of Gaussian pulses in non-dispersive dielectric layers

In this work, the first and second order effects for reflected and transmitted pulses with a Gaussian distribution of frequencies are analytically developed and interpreted. They show some peculiar characteristics that bear certain parallelism with those of monochromatic beams with a Gaussian distribution of amplitudes. However, when the former are considered, the results of the first and second order effects obtained analytically are more difficult to interpret and are clearly limited by the principle of causality. We show that pulses show some peculiar characteristics when they reflect and transmit through linear media: time delay, shifting of the mean frequency and modification of the pulse width. In addition to these effects we show and analyze the unexpected presence of chirping when a simple structure of non-dispersive materials is considered.

On Focusing of Broadband Terahertz Pulses

The particular features of the focusing of a broadband THz pulse with a Gaussian transverse amplitude distribution by a lens are investigated theoretically. The expressions for the spatiotemporal field distribution on the beam axis and in the focal plane of the lens are obtained in the quasi-optical approximation. It is shown that, for the focusing to be efficient, it is necessary to use lenses with a focal distance that is much shorter than the characteristic diffraction length at the frequency corresponding to the spectral maximum of the THz pulse.

WADA-W: A Modified WADA SNR Estimator for Audio-Visual Speech Recognition

One of the main challenges in speech recognition is developing systems that are robust to contamination by intrusive background noise. In audio-visual speech recognition (AVSR), audio information is augmented by visual information in order to help improve the performance of speech recognition, particularly when the audio modality is so significantly corrupted by background noise and it becomes hard to differentiate the original speech signal from the noise. The signal-to-noise ratio (SNR) can be used to identify the level of noise in original speech signal and one widely used method for SNR estimation is waveform amplitude distribution analysis (WADA), which is based on the assumption that the speech and noise signals have Gamma and Gaussian amplitude distributions respectively. Based on previous approaches, this work uses a precomputed look-up table as a reference for SNR estimation. In this study, WADA-white (WADA-W) has been developed, which rebuilds the precomputed look-up table using a white noise profile in combination of our own AVSR database. This new data corpus, namely the Loughborough University Audio-Visual (LUNA-V) dataset that contains recordings of 10 speakers with five sets of samples uttered by each speaker is used for this experimental work. We evaluate the performance of WADA-W on this database when it is corrupted by noise generated from three profiles obtained from the NOISEX-92 database included at varying SNR values. Evaluation of performance using the LUNA-V database shows that WADA-W performs better than the original WADA in terms of SNR estimation.

Emulating the Statistical Properties of Indoor Power Line Colored Background Noise for Development of a Power Line Noise Simulator

This paper deals with the development of a realistic power line channel simulator wherein power line communication devices can be tested before implementation to meet the massive need of data transfer. The statistics of the noise follow the experimentally observed in different sites, namely the time-varying non-white power spectral densities (PSDs) of the background noise and a target non Gaussian amplitude distribution. The procedure based on the inverse cumulative distribution function method of generation of random numbers and iteratively updating a target spectrum necessitates knowledge of a maximum of 17 parameters for successful implementation and has been validated for three sites in the low-frequency ([Formula: see text]500[Formula: see text]kHz) and high-frequency (1–30[Formula: see text]MHz) bands. The average percentage errors in prediction of the mean of the channel capacity (CC) are 12.68% and 10.66% in the two bands, respectively. The minimum correlations of the distribution of BER of OFDM in a channel corrupted by the simulated and observed noises are is 0.883 and 0.801 in the two bands which are high compared to 0.422 and 0.355, respectively, when the requirement of a target amplitude distribution is neglected. With low-frequency noise emulated by a data acquisition card, an average percentage error of 11.82% in the CC and a correlation of 0.867 (against 0.498) in BER are obtained. The noise thus generated can be used as a testbed for system testing, instead of the conventional static models (additive white Gaussian noise or with time-invariant colored PSD), leading to better optimization of the implemented devices.

On Bussgang’s Theorem, Separability, and Colored Random Phase Multisines

Random phase multisines tend asymptotically, with an increasing number of harmonics and irrespective of their spectral coloring, to the Gaussian amplitude distribution and can be used as an alternative to Gaussian signals to measure the best linear approximation (BLA) of nonlinear systems. The asymptotic error on the measured frequency characteristics, compared to that measured with Gaussian noise, is of order $O(M^{-1})$ , where $M$ is the number of harmonics. Flat (white) multisines are still a better approximant to Gaussian noise, because even in a nonasymptotic setting ( $M$ is low), the measured BLA of a static nonlinearity remains static. This is due to the fact that both Gaussian noise and flat random phase multisines are separable signals. Random phase multisines with a nonflat spectral coloring, however, are nonseparable signals and introduce dynamics to the BLA of a static nonlinearity, which was observed for a low harmonic number. Due to this reason, usually, only flat random phase multisines are used in the applications. In this paper, we investigate more deeply this phenomenon, performing an order $O(M^{-2})$ analysis of the approximation error. We show that the dynamics of the error depend, in a simple way, on the spectral coloring and this effect is decaying quickly with increasing $M$ . We conclude, in consequence, that colored random phase multisines are asymptotically a good working alternative to Gaussian noise and even a better choice for an excitation than flat random phase multisines due to more freedom in a signal design.

О фокусировке широкополосных терагерцовых импульсов

AbstractThe particular features of the focusing of a broadband THz pulse with a Gaussian transverse amplitude distribution by a lens are investigated theoretically. The expressions for the spatiotemporal field distribution on the beam axis and in the focal plane of the lens are obtained in the quasi-optical approximation. It is shown that, for the focusing to be efficient, it is necessary to use lenses with a focal distance that is much shorter than the characteristic diffraction length at the frequency corresponding to the spectral maximum of the THz pulse.

Distortions of Gaussian pulses transmitted through a transparent isotropic layer

Los láseres pueden operar en dos regímenes: modo continuo ó pulsado. En los casos más simples, el modo continuo se corresponde a haces monocromáticos con distribución de amplitudes gaussiana (es un haz limitado en el espacio); mientras que el modo pulsado corresponde a haces policromáticos con distribución gaussiana de frecuencias (pulso limitado en el tiempo).Cuando los haces pulsados se reflejan y refractan en diferentes tipos de interfaces, sufren distorsiones peculiares que tienen cierto paralelismo con los encontrados para haces limitados en el espacio. Estos efectos, como se muestra en un trabajo anterior, corresponden al retardo de tiempo (primer orden) y al cambio de ancho de pulso (segundo orden).Las distorsiones están claramente limitadas por el principio de causalidad y su interpretación, aunque no es directa, emerge claramente cuando los campos asociados se expresan en magnitud y fase. Pero como las expresiones analíticas no son simples (incluso en el caso de que el pulso se transmita a través de una capa única de material lineal, homogéneo, isotrópo y transparente) se hace difícil resolver el problema inverso.En este trabajo, presentamos un desarrollo analítico alternativo que hace posible determinar explícitamente estos efectos de distorsión cuando un pulso incide normalmente en una capa isotrópica transparente sumergida en un medio de características análogas.

Design and Experimental Verification of a Compact Gaussian Beam Source for Parallel-Plate Waveguide Tests

We present a compact and efficient electromagnetic source able to generate a 2-D Gaussian beam in a parallel-plate waveguide. The parallel-plate waveguide is a typical guiding structure used to experimentally test in a laboratory the electromagnetic behavior of a device under test in terms of propagation, transmission, and reflection. The most common launcher for this waveguide is a quarter-wavelength monopole, which generates a cylindrical wave. However, in order to approximate the cylindrical wave to a plane-wave impinging on the device under test, this launcher needs electrically large setups. The proposed solution makes use of a metallic bidimensional parabolic reflector, which is able to transform the cylindrical wave radiated by the conventional launcher into a plane wave with the Gaussian amplitude distribution. We demonstrate that this setup can dramatically reduce the dimensions of a conventional launcher for a given directivity (i.e., planarity of the generated phase fronts). The optimum design and the experimental verification of the proposed compact launcher are presented.

Mesoscopic fluctuation in a multilevel quantum dot in the Kondo regime

We study the mesoscopic fluctuation in a multilevel quantum dot on account of the disorder. In the regime of strong Coulomb blockade, statistically independent multilevel contributes to suppression of a single-particle level fluctuation near the mixed valence regions and this results in a narrow Gaussian distribution of an effective tunneling amplitude.

Deriving fatigue equivalent power spectral density spectra for the vibration testing of engine components

AbstractVibration testing for the proof of structural durabilty often is performed on the basis of power spectral density spectra. At present, there are large uncertainties concerning the derivation of appropriate spectra for fatigue testing. Especially for non‐periodic, non‐stationary excitations, the commonly used procedures based on the fast Fourier transformation usually yield inaccurate results. Additional problems arise if the analyzed signals do not follow a Gaussian amplitude distribution, which is a prerequisite for describing a time history as a random process with a power spectral density. To overcome these problems, the FatiResponse method for deriving fatigue equivalent power spectral density spectra was developed and is presented here. It takes into account both the possible dynamic and fatigue responses of virtual structures. Shock response and fatigue response spectra are used to describe the impact of an arbitrary signal on virtual structures having virtual critically loaded locations. From these, test spectra are derived that yield the same shock and fatigue responses as the measured vibrations. The method is explained and demonstrated using vibration data of a passenger car engine consisting of harmonic and stochastic excitations. The procedure is validated using a dummy structure and compared to commonly used procedures.

The set-down and set-up of directionally spread and crossing surface gravity wave groups

For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above $30{-}40^{\circ }$ ($21{-}28^{\circ }$ for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of $50{-}70^{\circ }$ and above, which are known to occur in the ocean.

Modeling nonlinear Rayleigh wave fields generated by angle beam wedge transducers—A theoretical study

Nonlinear Rayleigh wave fields generated by an angle beam wedge transducer are modeled in this study. The calculated area sound sources underneath the wedge are used to model the fundamental Rayleigh sound fields on the specimen surface, which are more accurate than the previously used line sources with uniform or Gaussian amplitude distributions. A general two-dimensional nonlinear Rayleigh wave equation without parabolic approximation is introduced and the solutions are obtained using the quasilinear theory. The second harmonic Rayleigh wave due to material nonlinearity is given in an integral expression with these fundamental Rayleigh waves radiated by the wedge transmitter acting as a forcing function. Multi-Gaussian beam (MGB) models are employed to simplify these integral solutions and to extract the diffraction and attenuation correction terms explicitly. The effect of nonlinearity of generating sources on the second harmonic Rayleigh wave fields is taken into consideration; simulation results show that it will affect the magnitude and diffraction correction of the second harmonic waves in the region close to the Rayleigh wave sound sources. This research provides a theoretical improvement to alleviate the experimental restriction on analyzing the effects of diffraction, attenuation and source nonlinearity when using angle beam wedge transducers as transmitters.

Splitting and accelerating Gaussian beam modulated by Mittag Leffler function

We propose and demonstrate the generation of a Mittag–Leffler Gaussian beam (MLG) throughout the modulation of a Gaussian beam with Mittag–Leffler (ML) complex function. This beam presents splitting and accelerating properties. The key element of our method is the use of a ML function of complex variable. The amplitude distribution of this Mittag–Leffler–Gaussian beam is symmetric and has multiple components with petal shape. Each of these petals has an elliptical Gaussian amplitude distribution and a curved trajectory.