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Baleen whales produce a wide variety of frequency-modulated calls. Extraction of the time–frequency (TF) structures of these calls forms the basis for many applications, including abundance estimation and species recognition. Typical methods to extract the contours of whale calls from a spectrogram are based on the short-time Fourier transform and are, thus, restricted by a fixed TF resolution. Considering the low-frequency nature of baleen whale calls, this work represents the contours using a pseudo-Wigner–Ville distribution for a higher TF resolution at the cost of introducing cross terms. An adaptive threshold is proposed followed by a modified Gaussian mixture probability hypothesis density filter to extract the contours. Finally, the artificial contours, which are caused by the cross terms, can be removed in post-processing. Simulations were conducted to explore how the signal-to-noise ratio influences the performance of the proposed method. Then, in experiments based on real data, the contours of the calls of three kinds of baleen whales were extracted in a highly accurate manner (with mean deviations of 5.4 and 0.051 Hz from the ground-truth contours at sampling rates of 4000 and 100 Hz, respectively) with a recall of 75% and a precision of 78.5%. [ABSTRACT FROM AUTHOR]

The two-dimensional (2D) active target localization is generally hindered by the high temporal and spatial sidelobe levels in snapshot-deficient scenarios, where the adaptive approaches undergo performance degeneration since they require many snapshots to build the sample covariance matrix. Aiming at working robustly in snapshot-deficient active scenarios, a 2D expectation-maximization-based vertical-time-record (EMVTR) approach is proposed to compensate for the snapshot deficiency and achieve the high-resolution active localization by reconstructing the covariance matrix using estimated hyperparameters, i.e., signal powers and noise variance. With the short-time Fourier transform, the proposed approach could reduce echoes' temporal correlation and attain robust beam-time localization in mild reverberation. The multi-frequency EMVTR is derived from the single-frequency case to improve the weak echo localization. The performance is evaluated by considering single and multiple target echoes in simulation and a single moving target with tank experimental data. The results manifest the proposed EMVTR's robustness and effectiveness for the 2D active localization in snapshot-deficient scenarios. [ABSTRACT FROM AUTHOR]

An analytical and numerical Fourier transform based approach is presented to investigate the space-time dependence for the longitudinal velocity resulting from the longitudinal impact force excitation of viscoelastic rods with lateral inertia. A one-dimensional dissipative Rayleigh-Love wave equation including material memory, dissipation, and/or transverse effects due to Poisson coupling is developed from a generic model of the time dependent stress strain relationship for the rod material. A Gaussian signal with a suitable time scale is used to represent the hammer impact forces. Fourier transform, standing wave, and modal methods are utilized to develop analytical solutions for the longitudinal velocity resulting from the impact excitation of semi-infinite and finite length free-free elastic rods with no transverse effects to provide a baseline and segue to analogous results for viscoelastic rods with transverse effects. Numerical results from an FFT approach are presented to illustrate the effects of material losses and transverse effects on attenuation and dispersion in viscoelastic rods using the Kelvin-Voigt model for the constitutive equation of the rods. [ABSTRACT FROM AUTHOR]

This paper proposes a method for displaying the phase information in speech signals through group delay spectrogram, without the need for phase unwrapping. The method involves scaling down the phase values without affecting the shape of the phase or group delay function, thus preserving the information of the phase spectrum. This is accomplished using single-frequency filtering (SFF) of speech signals to obtain the instantaneous complex SFF spectrum. The SFF involves filtering a frequency-shifting signal using a resonator at half the sampling frequency. The SFF spectrum displays characteristics similar to the standard short-time Fourier transform (STFT) spectrum, but without the effects of truncation due to windowing operation. The objective of the present study is to show that features of speech production can also be observed in the phase information, displayed through the group delay spectrogram. The time–frequency resolution in the group delay spectrogram depends on the choice of the bandwidth of the resonator used in the SFF analysis. The speech production features displayed in the group delay spectrogram are examined for different types of speech signals at different time-frequency resolutions. [ABSTRACT FROM AUTHOR]

We consider a two-part method for computing the acoustic scattering T-matrix of a three dimensional particle. The first part involves accurately computing the far fields by solving a number of particular scattering problems. The second part calculates the T-matrix from these far fields using the Fourier transform over the sphere. The two-part method was first introduced in Ganesh and Hawkins [J. Comput. Appl. Math. 234, 1702–1709]. The focus of this work is to demonstrate the numerical stability and physical correctness of the two-part method for scattering by nonspherical particles with large aspect ratios and size parameters that are at the upper limit of numerical stability for the current state-of-the-art algorithm. The numerical stability of the method is attributed to elimination of the Hankel functions by working with the far field. The numerical experiments use our recently developed open-source software package (TMATROM3) that implements the two-part method. [ABSTRACT FROM AUTHOR]

An interferometric signal processing method for localizing a broadband moving sound source in an oceanic waveguide is proposed and studied theoretically and experimentally. The field of a moving sound source in waveguide creates a stable interference pattern of the intensity distribution (interferogram) I (ω , t) in the frequency-time domain. Sound intensity is accumulated along interference fringes over the observation time. The two-dimensional Fourier transform (2D-FT) is applied to analyze the interferogram I (ω , t). The result of the 2D-FT F (τ , ν) is called the Fourier-hologram (hologram). The mathematical theory of hologram structure F (τ , ν) is developed in the present paper. It is shown that the hologram F (τ , ν) allows the coherent accumulation of sound intensity of the interferogram in a relatively small area focal spots. The presence of these focal spots is the result of interference of acoustic modes with different wave numbers. The main result of this paper is a simple relationship between the focal spots coordinates on the hologram and the source range, velocity, and motion direction. The proposed interferometric signals processing method for source localization is validated using experimental observations and numerical modeling in the band 80–120 Hz. The estimations of source range, velocity, and motion direction are performed for different cases of source motion. [ABSTRACT FROM AUTHOR]

This paper develops an efficient three-dimensional (3D) underwater acoustic propagation model with multi-layered fluid seabeds based on the equivalent source method (ESM). It solves the Helmholtz equation exactly by a superposition of fields generated by equivalent sources. A linear system coupling ESM equations is derived by imposing boundary conditions and solved iteratively using the generalized minimum residual method. Unlike a direct ESM solver, matrix–vector products in each iteration are evaluated by a pre-corrected fast Fourier transformation (PFFT), significantly reducing the numerical cost and enabling efficient solution of 3D large-scale propagation. Moreover, sound speed profiles can be taken into account by dividing the water column into sub-layers, each of which requires an individual PFFT procedure using an FFT subgrid scheme. Simulations of propagation over a Gaussian canyon validate the PFFT-accelerated ESM (PFFT-ESM). The capability of the PFFT-ESM for 3D scattering problems is demonstrated by further presenting the Gaussian canyon simulations with corrugated surface waves. [ABSTRACT FROM AUTHOR]

There are various structures constructed with periodically stiffened thin plates. Vibration prediction of such structures is not easy compared to the structures comprised of uniform plates only due to the mathematical complexity stemmed from the periodic nature. This study provides the analytic method to predict the wave transmission at junctions connecting two semi-infinite periodic structures and the response of a finite periodic structure to an external harmonic point force. The same theoretical framework is employed for dealing with both phenomena. First, free wave solutions are obtained by solving the governing equation for the bending motion of a periodically stiffened, infinite plate using the spatial Fourier Transform and the Floquet's theorem. Then, the free wave solutions are linearly superposed, and the linear coefficients are calculated by applying the appropriate boundary conditions. Numerical simulation is conducted. In dealing with the periodic finite structure, the result is compared with that by the finite element analysis. It is revealed that the periodic nature of the structures affects both the energy transmission and the vibration response of the periodically stiffened plates. [ABSTRACT FROM AUTHOR]

A formulation based on the Fourier transform and generalized functions, and implemented with a fast Fourier transform, is developed to solve a classic acoustics problem: radiation from an unbaffled cylinder with flat endcaps. The endcaps as well as the cylindrical surface have a specified modal vibration pattern, and the problem is solved using the sum of two independent formulations based on the Fourier transform: (1) a vibrating cylinder with rigid endcaps and (2) a rigid cylindrical tube with vibrating diaphragms at its ends. The resulting nearfield solution correctly models the diffraction effects generated at the sharp ends of the cylinder. Calculation of the farfield radiated pressure follows directly from the nearfield solutions with a slight modification to the standard formulas. Results from the formulations are validated with a boundary element simulation and show excellent agreement with errors of less than 1%. [ABSTRACT FROM AUTHOR]

A better understanding of ultrasound scattering in a three-dimensional (3D) medium can provide more accurate methods for ultrasound tissue characterization. The possibility of using two-dimensional impedance maps (2DZMs) based on correlation coefficients has shown promise in the case of isotropic and sparse medium [Luchies and Oelze, J. Acoust. Soc. Am. 139, 1557–1564 (2016)]. The present study investigates the use of 2DZMs in order to quantify 3D scatterer properties of dense media from two-dimensional (2D) histological slices. Two 2DZM approaches were studied: one based on the correlation coefficient and the other based on the 2D Fourier transform of 2DZMs. Both 2DZM approaches consist in estimating the backscatter coefficient (BSC) from several 2DZMs, and then the resulting BSC was fit to the theoretical polydisperse structure factor model to yield 3D scatterer properties. Simulation studies were performed to evaluate the ability of both 2DZM approaches to quantify scattering of a 3D medium containing randomly distributed polydisperse spheres or monodisperse ellipsoids. Experimental studies were also performed using the histology photomicrographs obtained from HT29 cell pellet phantoms. Results demonstrate that the 2DZM Fourier transform–based approach was more suitable than the correlation coefficient–based approach for estimating scatterer properties when using a small number of 2DZMs. [ABSTRACT FROM AUTHOR]

Spectral estimation is a necessary methodology to analyze the frequency content of noisy data sets especially in acoustic applications. Many spectral techniques have evolved starting with the classical Fourier transform methods based on the well-known Wiener-Khintchine relationship relating the covariance-to-spectral density as a transform pair culminating with more elegant model-based parametric techniques that apply prior knowledge of the data to produce a high-resolution spectral estimate. Multichannel spectral representations are a class of both nonparametric, as well as parametric, estimators that provide improved spectral estimates. In any case, classical nonparametric multichannel techniques can provide reasonable estimates when coupled with peak-peaking methods as long as the signal levels are reasonably high. Parametric multichannel methods can perform quite well in low signal level environments even when applying simple peak-picking techniques. In this paper, the performance of both nonparametric (periodogram) and parametric (state-space) multichannel spectral estimation methods are investigated when applied to both synthesized noisy structural vibration data as well as data obtained from a sounding rocket flight. It is demonstrated that for the multichannel problem, state-space techniques provide improved performance, offering a parametric alternative compared to classical methods. [ABSTRACT FROM AUTHOR]

A vertical line array can be deployed in deep water below the critical depth, the depth where the sound speed equals the sound speed at the surface, to take advantage of the lower ambient noise level (compared with above the critical depth) for target detection. To differentiate a submerged source from a surface source, a Fourier transform based method [McCargar and Zurk, J. Acoust. Soc. Am. 133, EL320–325 (2013)] was proposed for a narrowband signal that exploits the depth-related harmonic (oscillation) feature of the beam power time series associated with the target arrival. In this paper, incoherent matched beam processing is used to estimate the target depth. Where the replica (calculated) beam intensity or amplitude time series best matches that of the data is used to estimate the source depth. This method is shown, based on simulated data, to provide a better depth resolution in general and better ability to estimate the depth of a very shallow source (say at 10 m) and can be used to complement the Fourier transform based method. It can be extended to process (random) broadband signals and to environments where the Lloyd's mirror theory is not valid. [ABSTRACT FROM AUTHOR]

Quantitative ultrasound techniques based on the parametrization of the backscatter coefficient (BSC) are used to characterize concentrated particle suspensions. Specifically, a scattering model is fit to the measured BSC and the fit parameters can provide local suspension properties. The scattering models generally assume an isotropic microstructure (i.e., spatial organization) of the scatterers, whereas the sheared concentrated suspensions can develop an anisotropic microstructure. This paper studied the influence of the shear-induced anisotropic microstructure of concentrated suspensions on the ultrasonic backscattering. Experiments were conducted on suspensions of polymethylmetacrylate spheres (5.8 μm in radius) sheared in a Couette flow device to obtain anisotropic microstructure and then mixed by hand to obtain isotropic microstructure. Experimental structure factors that are related to the spatial distribution of sphere positions were obtained by comparing the BSCs of one concentrated and one diluted suspension. Finally, Stokesian dynamics numerical simulations of sheared concentrated suspensions are used to determine the pair correlation function, which is linked to the Fourier transform of the structure factor. The experimental structure factors are found to be in good agreement with numerical simulations. The numerical simulation demonstrates that the angular-dependent BSCs and structure factors are caused by the shear-induced anisotropic microstructure within the suspension. [ABSTRACT FROM AUTHOR]

Acoustic instabilities are frequently the culprit for engine failure. To mitigate these instabilities, an accurate model of the nonlinear acoustic pressure profile of the system is necessary. This study develops a nonlinear model for the acoustic response of an area-contraction. The derivation begins with the unsteady Bernoulli equation which is formed into the pressure drop across the area-contraction. Each acoustic variable is assumed to be time-harmonic and is written as the sum of a steady and fundamental term. Using a Fourier transformation, nonlinear expressions for the pressure drop and impedance are derived as functions of the steady and acoustic velocity. These expressions capture the nonlinearity of the acoustic response when the flow can reverse out of the orifice, i.e., the amplitude of the mean velocity is less than the amplitude of the oscillating acoustic velocity. This impedance model is verified by archive quality acoustic response data from a previous study. [ABSTRACT FROM AUTHOR]

It remains an open question how well the increased bandwidth afforded by broadband echosounders can improve species discrimination in fisheries acoustics. Here, an objective statistical approach was used to determine if there is information available in dual channel broadband data (45–170 kHz) to allow discrimination between in situ echoes obtained from monospecific aggregations of three species (hake, Merluccius productus: anchovy, Engraulis mordax; and krill, Euphausiia pacifica) using a remotely operated vehicle. These data were used to explore the effects of processing choices on the ability to statistically classify the broadband spectra to species. This ability was affected by processing choices including the Fourier transform analysis window size, available bandwidth, and the method and scale of data averaging. The approach to normalizing the spectra and the position of individual targets in the beam, however, had little effect. Broadband volume backscatter and single target spectra were both used to successfully classify acoustic data from these species with ∼6% greater success using volume backscatter data. Broadband data were effectively classified to species while simulated multi-frequency narrowband data were categorized at rates near chance, supporting the presumption that greater bandwidth increases the information available for the characterization and classification of biological targets. [ABSTRACT FROM AUTHOR]

In order to incorporate a directive sound source into acoustic simulation using the finite-difference time-domain method (FDTD), this paper proposes an optimization-based method to estimate the initial value which approximates a desired directional pattern after propagation. The proposed method explicitly considers a discretized FDTD scheme and optimizes the initial value directly in the time domain so that every effect of the discretization error of FDTD, including numerical dispersion, is taken into account. It is also able to consider a frequency-wise directivity by integrating the Fourier transform into the optimization procedure, even though the estimated result is defined in the time domain. After the optimization, the obtained result can be utilized in any acoustic simulation based on the same FDTD scheme without modification because the result is represented as the initial value to be propagated and no additional procedure is required. [ABSTRACT FROM AUTHOR]

The purpose of this work is to find a method to locate the scattering centers in spatial domain; by using this information, the mean scatter spacing (MSS) can be estimated, and the spatial information is the one-dimensional imaging of scattering centers. This paper presents a method that can locate the scattering centers in spatial domain robustly and automatically. By incorporating it with fast Fourier transformation, the MSS can be estimated. The three foremost processes, matched filtering, envelope extraction, and peak reconstruction, are incorporated in the authors' algorithm. Monte Carlo simulations demonstrate that the proposed method is a robust one to locate scattering centers in spatial domain, and has a better performance than spectrum-based MSS estimation techniques. Especially exploited in estimating MSS which varies from 0.6 to 1.2 mm in the range of human mean trabecular bone spacing, the proposed method shows great potential in medical use. Simple but widely used phantom experiments demonstrate that the proposed algorithm has the capacity to locate scattering centers in spatial domain. [ABSTRACT FROM AUTHOR]

Leaky Lamb waves have the potential to be used to perform non-destructive testing on a set of several parallel and immersed plates. Short-time Fourier transform and two-dimensional Fourier transform have both been successfully used to measure the propagation properties: phase and group velocity, and leaky attenuation. Experimental measurements were validated by comparison between theory, experimentation and finite-element simulations (using comsol multiphysics® software) in the case of one immersed plate in water. These signal processing techniques proved to be efficient in the case of multi-modal propagation. They were applied to two immersed plates to identify the leaky Lamb mode generated in the second plate. Dispersion curves of the system composed by two immersed and parallel plates are computed. When plates have the same thickness, leaky Lamb modes propagate from the first to the second plate without any mode change, with the apparent attenuation being weaker in the second plate. Considering that the second plate is continuously supplied in energy by the first one, an energy-based model is proposed herein to estimate the apparent attenuation in the second plate. Despite our extremely simplifying assumption, this model proved to be in good agreement with both finite-element modelling and experimentation. [ABSTRACT FROM AUTHOR]

The diffraction of a spherical sound wave by a thin hard half-plane is considered. The total field at any position in the space surrounding the edge of the half-plane is composed of three components, two of which are expressed from pure geometrical considerations, and a third component which seems to originate from fictive sound sources situated on the edge of the half plane. This paper takes the expression of the edge-diffracted field as formulated in the Biot-Tolstoy theory of diffraction for the case of a doublet sound signal emanating from the sound source [Biot and Tolstoy (1957). J. Acoust. Soc. Am. 29, 381–391] but rearranged later in a more tractable form by Medwin [(1981). J. Acoust. Soc. Am. 69, 1060–1064] for the more general case of a Dirac-like pulse. Hence a development in the frequency domain of the Fourier transform of the exact expression of the edge-diffracted field in the time domain takes into consideration a part with known special mathematical functions, and a part containing a serial development. This latter also expressed in some special mathematical functions, converges quite rapidly to the numerical Fourier transform of the exact time-domain expression. The presented solution may be used as a good approximation in simulations and in real case predictions of sound attenuation by thin hard barriers. [ABSTRACT FROM AUTHOR]

This study provides an argument cautioning against the use of adaptive-beamforming (ABF) techniques in conjunction with a known method for estimating the bottom reflection loss from natural marine ambient noise. This application of ABF has been investigated in the past with rather inconsistent results. Furthermore, no formal proof that ABF algorithms do indeed provide an estimate of the bottom reflection loss is available. This study moves from a recent derivation of the relationship between the bottom reflection coefficient and the Fourier transform of the marine-noise spatial coherence function. The circumstances under which the beamforming operation approximates a discrete Fourier transform (DFT) of the spatial coherence function estimated from array data are analyzed. It is shown that, under certain conditions, conventional beamforming is equivalent to directly computing the DFT of the coherence function, as long as some subtle details are properly taken into account. Furthermore, it is shown that ABF cannot be guaranteed, in general, to perform this operation, and therefore provide an estimate of the bottom reflection coefficient. The conclusions are demonstrated on simulated and measured data. [ABSTRACT FROM AUTHOR]

The vibroacoustic behavior of an infinitely long cylindrical shell with periodic lengthwise ribs is studied. The shell motion is described by the Donnell equations, and the lengthwise rib is modeled as an elastic beam whose motion is decomposed into longitudinal and flexural vibrations. Analytical expressions are obtained for the shell motion via a circumferential mode expansion based on the periodicity in the circumferential direction and the Fourier transform in the longitudinal direction. Furthermore, the far-field radiated pressure is obtained via the stationary-phase approach. The shell vibration and sound radiation are analyzed using discrete circumferential wavenumbers. Multi-order flexural Bloch waves exist in the circumferential direction when the cylindrical shell is equipped with periodic lengthwise ribs. The supersonic components of the flexural Bloch waves radiate efficiently and lead to acoustic radiation resonances in the far field. [ABSTRACT FROM AUTHOR]

Passive fathometry is a technique whereby broadband ambient ocean noise received on an array of hydrophones is averaged and cross-correlated to produce a sub-bottom profile [Siderius, Harrison, and Porter (2006). J. Acoust. Soc. Am. 120, 1315–1323]. Here this technique is extended to determine the vertical velocity of the array, and compensate for it, without any prior knowledge, i.e., Doppler Passive Fathometry. For Fourier transform lengths beyond a certain limit, the differing Doppler between the direct and bottom reflected paths spoils the correlation match, however it is shown by using some experimental data, where the array was known to suffer from arbitrary but near periodic motion, that compensation is possible, enabling continuing time integration. In the process, the vertical velocity becomes known. Velocity, with peak value ∼±1 m/s, is plotted against time and shown to be 90° out of phase with depth, as expected for periodic motion. Since stationary targets have already been detected by noise correlation [Harrison (2008). J. Acoust. Soc. Am. 123, 1834–1837], it is implied that the range of moving targets can also be determined. [ABSTRACT FROM AUTHOR]

Near-field error sensing is beneficial to the compactness and stability of an active noise control system. This paper proposes an error sensing strategy based on the spatial Fourier transform to achieve active directivity control of radiated sound. The error microphone array is located on a plane close to the primary source and the cost function is the weighted sum of the error signals from the microphones. The weighting factor is related to the phase shift from the error microphones to the plane perpendicular to the direction where noise reduction is required. The geometric configurations of the error microphone array for effective directivity control are investigated. It is found that the distance between neighboring error microphones must be less than approximately half the wavelength of the frequency of interest and the equivalent size of the microphone array should be larger than twice the size of the primary source. Numerical simulations and experiments demonstrate the feasibility of the proposed strategy. [ABSTRACT FROM AUTHOR]

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration. [ABSTRACT FROM AUTHOR]

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays. [ABSTRACT FROM AUTHOR]

In this paper, a numerical wave field injection technique for characterizing the reflection coefficient of a planar medium interface is proposed. By injecting recorded wave field quantities into a three-dimensional (3D) finite-difference calculation, two key objectives are addressed: first, the recorded wave field is separated into its incident and reflected constituents without the need of spatial Fourier transforms or a temporal separation of incident and reflected parts in the recorded data. Second, the separated constituents are independently extrapolated to the location of the reflecting interface to determine its reflecting properties. The methodology is experimentally validated on 3D laboratory data consisting of reflections from the water-air interface in a water tank and is shown to give accurate results for incidence angles of up to 60°. [ABSTRACT FROM AUTHOR]

A dolphin's biosonar may effectively discriminate subtle differences among targets. In order to investigate the possible physical mechanism of target discrimination, in this study, a finite element model excited by a biomimetic click pulse was proposed. The acoustic scattering field and stress distribution of a stainless steel shell were simulated. The biomimetic click experiments were then conducted to verify the theoretical predictions in an anechoic tank. The experimental results showed a good agreement with the model simulations. Furthermore, the elastic time-frequency features of three cylindrical shells with different wall thickness were obtained using a fractional Fourier transform filter to eliminate specular reflection and cross-term interference. To compare discrimination capacity of the time-frequency features with and without the specular reflection, a time-frequency correlator was applied to calculate the correlation coefficient between different shells. The results indicated that the time-frequency features can be represented in high resolution with less cross-term interference, and these features without specular reflection showed a good capacity to discriminate the shells with different wall thickness. [ABSTRACT FROM AUTHOR]

The radiative transfer equation (RTE) is outlined and then applied to forest acoustics. The RTE is an integro-differential equation for the radiance, which is the angular Fourier transform of the spatial correlation function of the sound field. It correctly accounts for propagation phenomena such as multiple scattering, absorption, and the transformation of the coherent sound field into the incoherent field. In this formulation, acoustical properties of a forest are described by the total cross sections and differential scattering cross sections of different scatterers. In this paper, the four-layer forest model is used with the following distinct layers: ground, trunk layer, canopy layer, and open air. The trunk layer is modeled with finite vertical cylinders, while the canopy layer is modeled with diffuse scatterers. The total and differential scattering cross sections in these layers are calculated. The boundary condition for the radiance at the interface between the ground and trunk layers is formulated. Using a modified Born approximation, the RTE is solved for a plane sound wave normally incident on the edge of a forest. The mean intensities transmitted and backscattered from a stand of trees are calculated and analyzed. [ABSTRACT FROM AUTHOR]

A chirp signal is a signal with linearly varying instantaneous frequency over the signal bandwidth, also known as a linear frequency modulated (LFM) signal. It is widely used in communication, radar, active sonar, and other applications due to its Doppler tolerance property in signal detection using the matched filter (MF) processing. Modern sonar uses high-gain, wideband signals to improve the signal to reverberation ratio. High gain implies a high product of the signal bandwidth and duration. However, wideband and/or long duration LFM signals are no longer Doppler tolerant. The shortcoming of the standard MF processing is loss of performance, and bias in range estimation. This paper uses the wideband ambiguity function and the fractional Fourier transform method to estimate the target velocity and restore the performance. Target velocity or Doppler provides a clue for differentiating the target from the background reverberation and clutter. The methods are applied to simulated and experimental data. [ABSTRACT FROM AUTHOR]

Small aperture arrays (size less than a wavelength) can be used for passive angle of arrival (AOA) estimation of both broadband and narrowband signals in the frequency domain. Phase differences across the array are measured in the frequency domain and can be spectrally averaged if desired for stationary source AOA and frequencies. The array is capable of measuring multiple target AOAs so long as each target produces unique frequencies or radiates in unique frequency bandwidths. Broadband and narrowband signals from targets can be collected from the fast Fourier transform (FFT) bins and summed by arrival angle in elevation and azimuth using a bearing histogram where the amplitude is displayed in dB. This provides a very useful and intuitive display of received signal levels. The Cramer–Rao lower bound (CRLB) for bearing accuracy is presented as a function of frequency, aperture, and signal-to-noise ratio (SNR). The small aperture background noise includes any other coherent or incoherent signal other than the source of interest. Analysis of phase calibration requirements, nonstationary frequencies, and channel cross-talk are also presented, as well as a technique for generating broadband source signals with the fractional delays needed to simulate the correct AOA. [ABSTRACT FROM AUTHOR]

This paper describes a measurement technique that allows the modal amplitude distribution to be determined in ducts with mean flow and reflections. The method is based only on measurements of the acoustic pressure two-point coherence at the duct wall. The technique is primarily applicable to broadband sound fields in the high frequency limit and whose mode amplitudes are mutually incoherent. The central assumption underlying the technique is that the relative mode amplitude distribution is independent of frequency. The two-microphone method proposed in this paper is also used to determine the transmitted sound power and far field pressure directivity. [ABSTRACT FROM AUTHOR]

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified. [ABSTRACT FROM AUTHOR]

Underwater target elastic acoustic scattering and other acoustic scattering components are aliasing together in the time and frequency domains, and the existing signal processing methods cannot recognize the elastic scattering features under the aliasing condition because of the resolution limitation. To address this problem, this study, which is based on the target echo highlight model, analyzes the characteristics of target acoustic scattering components when the transmitted signal is a linear frequency modulation pulse. The target acoustic scattering structure in the fractional Fourier transform (FRFT) domain is deduced theoretically. Then, filtering is used in the FRFT domain to separate the target elastic acoustic scattering components. In addition, noise suppression performance and filter resolution are discussed. The target rigid and elastic acoustic scattering components are separated. Experimental results show that filtering in the FRFT domain can separate the elastic scattering components from the target echoes. Moreover, separated elastic acoustic scattering components have consistent theoretical features, which lay the foundation for studying the elastic scattering characteristics further. [ABSTRACT FROM AUTHOR]

Thermo-acoustic (TA) transducers are generation of sound speakers without any mechanical vibration system which exhibit an extremely wide frequency response range. In this paper, acoustic field responses to broadband input signals applied to both free-standing and nano-thinfilm-substrate thermo-acoustic devices are developed theoretically by using the Fourier transformation. A series of signals, including single-frequency signal, square root signal, periodic triangle wave signal, and periodic rectangular pulse signal, are applied to these TA devices in simulations and the acoustic pressure responses are investigated. The reproducibility of input signals is predicted. The single frequency results show good agreement with previously published experimental results. Alternative methods for reproducing the original signals with small distortion and low power consumption are introduced. The excellent performance of the TA devices on broadband signal responses will provide a design approach for sound parametric array and underwater communication equipment. [ABSTRACT FROM AUTHOR]

The time-domain Helmholtz-Kirchhoff (H-K) integral for surface scattering is derived for a refractive medium, which can handle shadowing effects. The starting point is the H-K integral in the frequency domain. In the high-frequency limit, the Green's function can be calculated by ray theory, while the normal derivative of the incident pressure from a point source is formulated using the ray geometry and ray-based Green's function. For a corrugated pressure-release surface, a stationary phase approximation can be applied to the H-K integral, reducing the surface integral to a line integral. Finally, a computationally-efficient, time-domain H-K integral is derived using an inverse Fourier transform. A broadband signal scattered from a sinusoidal surface in an upwardly refracting medium is evaluated with and without geometric shadow corrections, and compared to the result from a conventional ray model. [ABSTRACT FROM AUTHOR]

Generating acoustically bright and dark zones using loudspeakers is gaining attention as one of the most important acoustic communication techniques for such uses as personal sound systems and multilingual guide services. Although most conventional methods are based on numerical solutions, an analytical approach based on the spatial Fourier transform with a linear loudspeaker array has been proposed, and its effectiveness has been compared with conventional acoustic energy difference maximization and presented by computer simulations. To describe the effectiveness of the proposal in actual environments, this paper investigates the experimental validation of the proposed approach with rectangular and Hann windows and compared it with three conventional methods: simple delay-and-sum beamforming, contrast maximization, and least squares-based pressure matching using an actually implemented linear array of 64 loudspeakers in an anechoic chamber. The results of both the computer simulations and the actual experiments show that the proposed approach with a Hann window more accurately controlled the bright and dark zones than the conventional methods. [ABSTRACT FROM AUTHOR]

An efficient boundary element formulation is proposed to solve three-dimensional exterior acoustic scattering problems with multi-directional periodicity. The multi-directional periodic acoustic problem is represented as a multilevel block Toeplitz matrix. By exploiting the Toeplitz structure, the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced. The generalized minimal residual method is implemented to solve the linear system of equations. To efficiently calculate the matrix-vector product in the iterative algorithm, the original matrix is embedded into a multilevel block circulant matrix. A multi-dimensional discrete Fourier transform is then employed to accelerate the matrix-vector product. The proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space. Two case studies involving sonic crystal barriers are presented. In the first case study, a sonic crystal barrier comprising rigid cylindrical scatterers is modeled. To demonstrate the effectiveness of the proposed technique, periodicity in one, two, or three directions is examined. In the second case study, the acoustic performance of a sonic crystal barrier with locally resonant C-shaped scatterers is studied. [ABSTRACT FROM AUTHOR]

The numerical simulation of acoustic scattering from elastic objects near a water-sand interface is critical to underwater target identification. Frequency-domain methods are computationally expensive, especially for large-scale broadband problems. A numerical technique is proposed to enable the efficient use of finite-difference time-domain method for broadband simulations. By incorporating a total-field/scattered-field boundary, the simulation domain is restricted inside a tightly bounded region. The incident field is further synthesized by the Fourier transform for both subcritical and supercritical incidences. Finally, the scattered far field is computed using a half-space Green's function. Numerical examples are further provided to demonstrate the accuracy and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

For the enhancement of single-channel speech corrupted by acoustic noise, recently short-time Fourier transform domain clean speech estimators were proposed that incorporate prior information about the clean speech spectral phase. Instrumental measures predict quality improvements for the phase-aware estimators over their conventional phase-blind counterparts. In this letter, these predictions are verified by means of listening experiments. The phase-aware amplitude estimator on average achieves a stronger noise reduction and is significantly preferred over its phase-blind counterpart in a pairwise comparison even if the clean spectral phase is estimated blindly on the noisy signal. [ABSTRACT FROM AUTHOR]

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal as a linear superposition of as few spectral components as possible, without affecting the quality of the reproduction. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the fast Fourier transform. The achieved sparsity is theoretically equivalent to that rendered by the orthogonal matching pursuit (OMP) method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard OMP algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral representation is illustrated by comparison with the traditional method, in the line of the short time Fourier transform, involving only the corresponding orthonormal trigonometric basis. [ABSTRACT FROM AUTHOR]

In this paper, four delay-and-sum (DAS) beamformers formulated in the modal domain and the space domain for open and solid spherical apertures are examined through numerical simulations. The resulting beampatterns reveal that the mainlobe of the solid spherical DAS array is only slightly narrower than that of the open array, whereas the sidelobes of the modal domain array are more significant than those of the space domain array due to the discrete approximation of continuous spherical Fourier transformation. To verify the theory experimentally, a three-dimensionally printed spherical array on which 32 micro-electro-mechanical system microphones are mounted is utilized for localization and separation of sound sources. To overcome the basis mismatch problem in signal separation, source localization is first carried out using minimum variance distortionless response beamformer. Next, Tikhonov regularization (TIKR) and compressive sensing (CS) are employed to extract the source signal amplitudes. Simulations and experiments are conducted to validate the proposed spherical array system. Objective perceptual evaluation of speech quality test and a subjective listening test are undertaken in performance evaluation. The experimental results demonstrate better separation quality achieved by the CS approach than by the TIKR approach at the cost of computational complexity. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a method to mitigate ground surface vibration through a flex-ural plate coupled to the ground and acting as a horizontal wave barrier. Using the thin plate hypothesis, two flexural plates are coupled to the ground, the first plate being the excited plate and the second plate the horizontal wave barrier. For instance, the first plate may represent a slab track and be excited by the tramway wheels. A solution to the problem can be found using a spatial two-dimensional Fourier transform of the elastodynamics equation for the ground and a modal decomposition for the flexural plate vibration. The authors show that vibration is substantially mitigated by the horizontal wave barrier and depends on its thickness and width. When the top surface wavelength becomes smaller than twice the plate width, the horizontal wave barrier acts as a wave barrier in the frequency range of interest, i.e., from 20 Hz. [ABSTRACT FROM AUTHOR]

In shallow water zones and at low frequency, seabed and water column properties can be estimated from the acoustic wavenumbers using inversion algorithms. When considering horizontal line arrays (HLA) and narrowband sources, the wavenumbers can be evaluated with classic spectral analysis methods. In this paper, a compressed sensing (CS) method for sparse recovery of the wavenumbers is proposed. This takes advantage of the few propagating modes and allows for spectral estimation when short HLA are used. The CS representation improves the wavenumber estimation, compared to the Fourier transform. However, for small arrays and several propagating modes, the CS generates interferences and does not allow proper wavenumber estimation. When considering broadband sources, it is possible to combine the wavenumbers estimated at several frequencies in order to build a frequency-wavenumber (f-k) representation. In this case, a post-processing tracking operation which improves the f-k resolution is presented. This relies on a general approach of waveguide physics and uses a particle filtering (PF) algorithm to track the wavenumbers. The consecutive use of CS and PF leads to a better wavenumber estimation. This methodology can be used for sources that are not at an end-fire position. It is illustrated by simulations and successfully applied on the Shallow Water 2006 data using the 32 sensor SHARK array. [ABSTRACT FROM AUTHOR]

When signals are recorded on a planar aperture with point emitters/detectors, from either a three-dimensional (3D) scattering potential or from a 3D spatially-incoherent source distribution, an integral equation arises containing the product of two Green's functions in the weak scattering limit (the Born approximation). This fundamental imaging equation for scatterers or sources is derived and solved analytically. [ABSTRACT FROM AUTHOR]

This study introduces a method to obtain the reverberation decay functions for narrow bands from the filtered time-windowed broadband room impulse responses. The method corresponds to the free decay process of the band-pass sound energy. The filtering process is independent of the band-pass filter phase responses and it reduces the filtering influence on the decay rates. It places no limit on the permissible product BT of the bandwidth B and the reverberation time T when evaluating the decay rates of the obtained decay functions. [ABSTRACT FROM AUTHOR]

An alternative pressure-sensor based method for estimating the acoustic intensity, the phase and amplitude gradient estimation (PAGE) method, is presented. This method uses the same hardware as the standard finite-difference method, but does not suffer from the frequency-dependent bias inherent to the finite-difference method. A detailed derivation of the PAGE method and the finite-difference method is presented. Both methods are then compared using simple acoustic fields. The ability to unwrap the phase component of the PAGE method is discussed, which leads to accurate intensity estimates above previous frequency limits. The uncertainties associated with both methods of estimation are presented. It is shown that the PAGE method provides more accurate intensity estimates over a larger frequency bandwidth. [ABSTRACT FROM AUTHOR]

The modal wavenumber of rectangular, simply supported, isotropic thin plates was theoretically shown to be related to the zeros in the wavenumber spectrum and not to the peaks, resulting in an error between the actual modal wavenumber and location of the wavenumber spectrum peak for low mode orders. This theoretical proof is confirmed by experimental results reported in this letter. [ABSTRACT FROM AUTHOR]

An analytical approach is investigated to model ground-plate interaction based on modal decomposition and the two-dimensional Fourier transform. A finite rectangular plate subjected to flexural vibration is coupled with the ground and modeled with the Kirchhoff hypothesis. A Navier equation represents the stratified ground, assumed infinite in the x- and y-directions and free at the top surface. To obtain an analytical solution, modal decomposition is applied to the structure and a Fourier Transform is applied to the ground. The result is a new tool for analyzing ground-plate interaction to resolve this problem: ground cross-modal impedance. It allows quantifying the added-stiffness, added-mass, and added-damping from the ground to the structure. Similarity with the parallel acoustic problem is highlighted. A comparison between the theory and the experiment shows good matching. Finally, specific cases are investigated, notably the influence of layer depth on plate vibration. [ABSTRACT FROM AUTHOR]

Fundamental constructs of information theory are applied to quantify the performance of iterated (sequential) Bayesian localization of a time-harmonic source in a range- and time-invariant acoustic waveguide using the segmented Fourier transforms of the received pressure time series. The nonlinear relation, defined by acoustic propagation, between the source location and the received narrowband spectral components is treated as a nonlinear communication channel. The performance analysis includes mismatch between the acoustic channel and the model channel on which the Bayesian inference is based. Source location uncertainty is quantified by the posterior probability density of source location, by the posterior entropy and associated uncertainty area, by the information gain (relative entropy) at each iteration, and by large-ensemble limits of these quantities. A computational example for a vertical receiver array in a shallow-water waveguide is presented with acoustic propagation represented by normal modes and ambient noise represented by a Kuperman--Ingenito model. Performance degradation due to noise-model mismatch is quantified in an example. Potential extensions to uncertain and stochastic environments are discussed. [ABSTRACT FROM AUTHOR]

The received Doppler signal of a stationary sensor, as emitted by a transiting acoustic source, is used to estimate source motion parameters, including speed, closest distance, rest frequency, and closest point of approach (CPA) time. First, the instantaneous frequency, amplitude, and CPA time are accurately estimated by the polynomial chirplet transform of the Doppler signal. Thereafter, the three other source motion parameters are obtained with a simplified amplitude-weighted nonlinear least squares method. The proposed scheme is successfully applied to the analysis of the characteristics of a moving truck. [ABSTRACT FROM AUTHOR]