Time-domain Counterparts Research Articles

The minimum-frequency property of complex trace analysis

A waveform has the property of minimum frequency if its instantaneous frequency equals the Hilbert transform of its instantaneous bandwidth plus the spectral low-cut frequency. Minimum frequency is characterized by an amplitude spectrum that is maximally skewed toward the low frequencies. The associated property of maximum frequency is characterized by an amplitude spectrum that is maximally skewed toward the high frequencies. Minimum and maximum frequency are the time-domain counterparts of the spectral properties of minimum and maximum delay. Many waveforms have the property of minimum frequency, such as the Ricker wavelet. Waveforms that have the property of maximum frequency include Klauder wavelets that emphasize high frequencies. Impulsive wavelets can have both minimum frequency and minimum delay. The properties of minimum and maximum frequency suggest time-variant measures to estimate the spectral low-cut and high-cut frequencies of seismic traces and produce an instantaneous frequency attribute that is free of spikes. The property of minimum frequency has long been known but remains unfamiliar to geophysics. It is explained in the context of complex trace analysis illustrated with seismic wavelets and traces.

Differential geometric guidance law design for varying-speed missile

A unified differential geometric guidance law (DGGL) design framework for varying-speed missiles against stationary targets is proposed in this paper. The varying-speed missile guidance model is established in the arc-length domain with the help of the classical differential geometry curve theory. It is strictly proven that DGGL is a natural and intuitive choice for varying-speed missiles when intercepting stationary targets since the influence of missile speed is directly eliminated in the guidance model and also during the guidance law design process. Hence, the guidance performance of DGGL will remain the same, no matter how the missile speed changes. After that, the error dynamics approach, which is widely used in the guidance law design field for constant-speed missiles in the time domain, is extended to the arc-length domain for DGGL design. Besides, the nonlinearity of the guidance model is fully considered when designing DGGL, hence the guidance errors caused by linearizations and small-angle assumptions are avoided. Then, taking the representative optimal error dynamics (OED) as an example, the corresponding OED-based DGGLs for zero-effort-miss-control, impact-angle-control, and flying-range-control are respectively derived. Finally, the derived illustrative guidance laws are simulated and compared with their time-domain counterparts to verify the effectiveness and superiority of the proposed unified DGGL design framework.

Phonocardiography (PCG)-based early detection of heart anomalies using deep learning

A simple-to-use and cost-effective Phonocardiography (PCG)-based system is proposed for the early detection of cardiovascular anomalies. A summary is provided related to the main results of a comparative study of various signal processing and deep learning techniques applied to PCG signals to automatically differentiate normal heart sounds from five types of common murmurs. Initial results indicate an average of over 92 % and 71 % heart anomaly detection and classification rates, respectively. This is accomplished using a 5-layer-Deep Neural Network (DNN) with 100 neurons per layer using the Hyperbolic Tangent (tanh) as an activation function. The Discrete Wavelet Transform (DWT) and Heart Sound Envelogram (HSE) were found to be best in respectively denoising and segmenting the PCG signal. Mel Frequency Cepstral Coefficients (MFCC) Features were found to outperform their Frequency and Time Domain counterparts and were used to train and run the DNN. The proposed system should be useful in providing early warnings and initial indications to potentially sick people directing them to cardiologists in order to pursue more accurate diagnostics, making it a handy home-care tool in the context of smart and preventive public health systems.

A Revisit on Impulsive Stimulated Raman Spectroscopy: Importance of Spectral Dispersion of Chirped Broadband Probe.

The usefulness of a chirped broadband probe and spectral dispersion to obtain Raman spectra under nonresonant/resonant impulsive excitation is revisited. A general methodology is presented that inherently takes care of phasing the time-domain low-frequency oscillations without probe pulse compression and retrieves the absolute phase of the oscillations. As test beds, neat solvents (CCl4, CHCl3, and CH2Cl2) are used. Observation of periodic intensity modulation along detection wavelengths for particular modes is explained using a simple electric field interaction picture. This method is extended to diatomic molecule (iodine) and polyatomic molecules (Nile blue and methylene blue) to assign vibrational frequencies in ground/excited electronic state that are supported by density functional theory calculations. A comparison between frequency-domain and time-domain counterparts, i.e., stimulated Raman scattering and impulsive stimulated Raman scattering using degenerate pump-probe pairs is presented, and most importantly, it is shown how impulsive stimulated Raman scattering using chirped broadband probe retains unique advantages offered by both.

Analysis of Deficient-Length Partitioned-Block Frequency-Domain Adaptive Filters

This paper studies the convergence behavior of the partitioned-block frequency-domain adaptive filters (PBFDAF) for under-modeling scenarios. We focus on a family of the overlap-save PBFDAF algorithms with 50% overlap, including both of the constrained and unconstrained versions. The stochastic analysis of the constrained and unconstrained algorithms is carried out individually due to their convergence differences. For each algorithm, the frequency-domain error vector and the update equations are transformed into the time-domain counterparts, so we can analyze their convergence behavior completely in the time domain. We present the mean and mean-square convergence behavior of the augmented weight-error vector, and we obtain the closed-form expressions for the learning curve and the steady-state solutions. Based on the solution of the steady-state weight-error vector, we analyze if each version of the PBFDAF algorithm converges to the true solution and the Wiener solution. The theoretical model gains new insights into the convergence behavior of the deficient-length PBFDAF algorithms. The computer simulations support the theoretical model very well.

On the Convergence Behavior of Partitioned-Block Frequency-Domain Adaptive Filters

Partitioned-block frequency-domain adaptive filter (PBFDAF) algorithms have become very popular, in particular, for acoustic signal processing. However, the stochastic behavior of PBFDAFs has not been extensively examined. This paper presents a comprehensive statistical analysis for a family of the overlap-save PBFDAF algorithms with 50% overlap, including the transient and steady-state performance. The frequency-domain equations of the PBFDAFs are transformed into the time-domain counterparts, which allows us to carry out the analysis completely in the time domain. By means of the independence assumption and vectorization operation, theoretical models for the mean and mean-square behavior of the PBFDAF algorithms are established without restricting the distribution of the inputs to being Gaussian. Specifically, the mean weight behavior and corresponding steady-state solution are provided. Closed-form expressions for the mean-square deviation (MSD) and mean-square error (MSE) are derived. The upper bound on the step size for the mean and mean-square stability of the PBFDAFs is specified. The theoretical model presents new insights into the convergence properties of the PBFDAFs with a sufficient number of coefficients. It was revealed that both the constrained and unconstrained PBFDAFs converge to the Wiener solution. However, the mean weight vector of the unconstrained PBFDAF algorithms cannot converge to the true solution for any inputs, while that of the constrained version can. The presented theory explains why the steady-state MSD of the unconstrained PBFDAF algorithm is larger than that of the constrained version but their minimum MSE is the same. Monte Carlo simulations provide very good support for our theory.

Stability of boundary element methods for the two dimensional wave equation in time domain revisited

This study considers the stability of time domain BEMs for the wave equation in 2D. We show that the question of stability of time domain BEMs is reduced to a nonlinear eigenvalue problem related to frequency domain integral equations. We propose to solve this non-linear eigenvalue problem numerically with the Sakurai-Sugiura method. After validating this approach numerically in the exterior Dirichlet problem, we proceed to transmission problems in which we find that some time domain counterparts of “resonance-free” integral equations in frequency domain lead to instability. We finally show that the proposed stability analysis helps to reformulate these equations to obtain stable numerical schemes.

Hierarchical Location Identification of Destabilizing Faults and Attacks in Power Systems: A Frequency-Domain Approach

An optimization-based data-driven approach is proposed to identify the unknown location(s) of destabilizing faults and attacks in power systems. The analysis in this paper kicks in at the critical moment where the presence of destabilizing fault or attack is detected within the power system; therefore, there is an immediate need to identify the location(s) of the affected generators or loads in order to enable proper and effective post-detection measures. The proposed method works in frequency-domain. It does not require prior knowledge about the number of affected location(s). It is accurate in identifying the correct locations and also in preventing false alarms. It is computationally more efficient than its time-domain counterparts. Importantly, it is well-suited to be implemented in a hierarchical fashion, with applications such as in wide area monitoring systems. Various case studies on IEEE 9 and IEEE 39 bus test systems verified the performance of the proposed algorithms.

Plane Wave Diffraction by Arbitrary-Angled Lossless Wedges: High-Frequency and Time-Domain Solutions

This paper concerns the diffraction phenomenon originated by a uniform plane wave impacting an arbitrary-angled lossless dielectric wedge with planar surfaces. The high-frequency diffraction coefficients are obtained by performing uniform asymptotic evaluations of the radiation integrals resulting from the physical optics approximation of the electric and magnetic equivalent surface currents located on the inner and outer faces of the wedge. The final expressions are in closed form and contain the standard transition function of the uniform theory of diffraction and the Fresnel reflection and transmission coefficients related to the geometrical optics propagation mechanisms. Moreover, they allow a simple physical interpretation of each contribution and they are easy to use and to implement in a computer code. The knowledge of such diffraction coefficients in the frequency domain permits to apply the inverse Laplace transform to obtain the time-domain counterparts, which enable the evaluation of the transient diffracted field originated by an arbitrary function plane wave.

Diffraction by a Structure Composed of Metallic and Dielectric 90° Blocks

This letter deals with the plane wave diffraction by a composite structure consisting of metallic and lossless dielectric 90° blocks, which are adjacent and share the edge. Such a problem is first tackled in the frequency domain, and the related diffraction coefficients are determined by exploiting the uniform asymptotic physical optics approach. The inverse Laplace transform is applied to obtain the time-domain counterparts, which can be used to compute the transient diffracted field due to an arbitrary function plane wave.

An Alternative Complexity Reduction Method for Partitioned-Block Frequency-Domain Adaptive Filters

Partitioned-block frequency-domain adaptive filters provide lower algorithmic complexity than their time-domain counterparts. However, for certain applications, it is desirable to reduce complexity even further. This can be achieved by reducing the complexity of the constraint, or linearization, of the circular correlations. Existing methods are either suboptimal or are not sufficiently flexible in terms of the design parameters. Therefore, an alternative complexity reduction method is proposed, which achieves near-optimal performance and which, in addition, is flexible in terms of the design parameters, as these can be arbitrarily chosen.

A Novel Efficient Nonstandard High-Order Finite-Difference Time-Domain Method Based on Dispersion Relation Analysis

A novel approach to get new high-order nonstandard finite-difference time-domain methods is proposed. By using different coefficients in electric field and magnetic field update equations, schemes up to order (2, 8) are derived. These new methods maintain comparable accuracy to the conventional high-order finite-difference time-domain counterparts while a reduction in computational cost is achieved. The dispersion and anisotropic behaviors of these new methods are investigated. Some numerical examples are studied to examine the accuracy and efficiency of the new method.

Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian

The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.

Fast approximate inversion of FDHEM data

Despite advances in computer speed and code efficiency, the most often employed interpretation method for frequency domain helicopterborne electromagnetic (FDHEM) data is still inversion with one-dimensional (1D) models. In areas where the lateral rate of change of conductivity is small, inversion with 1D models is justified and can be sufficient. These conditions are often found in hydrogeophysical investigations in a sedimentary environment. Even for 1D inversion, the task of inverting a survey volume of 100,000s of data points can be time-consuming, and more or less sophisticated approximate methods have been developed. These are often included in software packages used for data and model display and handling of geographical information, e.g. EMflow (Macnae et al., 1998), EMax (Fullagar and Reid, 2001), etc. A fairly comprehensive comparison between different inversion and transformation techniques used for FDHEM data is published in Sattel (2005). We present a fast approximate method for one-dimensional (1D) inversion of frequency domain data and apply it to frequency domain helicopterborne data from the Bookpurnong area of the Murray River, South Australia. The method is based on fast approximate forward computation of transient electromagnetic step responses and their derivatives with respect to the model parameters of a 1D model, and the frequency domain responses and derivatives are found through Fourier transformation of the time domain counterparts using Fast Hankel Transform filters. The inversion is carried out with multi-layer models in a state-of-the-art formulation of a least-squares iterative inversion scheme including explicit formulation of the model regularisation through a model covariance matrix. The approximate and ordinary 1D inversion approaches thus share the inversion formulation, the difference lying only in the forward mapping. The method is 30 times faster than ordinary inversion for a layered earth model and produces model sections of concatenated 1D models and contoured maps of mean conductivity in elevation intervals almost indistinguishable from those of ordinary inversion.

Joint Transceiver Design for MIMO Channel Shortening

Channel shortening equalizers can be employed to shorten the effective impulse response of a long intersymbol interference (ISI) channel in order, for example, to decrease the computational complexity of a maximum-likelihood sequence estimator (MLSE) or to increase the throughput efficiency of an orthogonal frequency-division multiplexing (OFDM) transmission scheme. In this paper, the issue of joint transmitter-receiver filter design is addressed for shortening multiple-input multiple-output (MIMO) ISI channels. A frequency-domain approach is adopted for the transceiver design which is effectively equivalent to an infinite-length time-domain design. A practical space-frequency waterfilling algorithm is also provided. It is demonstrated that the channel shortening equalizer designed according to the time-domain approach suffers from an error-floor effect. However, the proposed techniques are shown to overcome this problem and outperform the time-domain channel shortening filter design. We also demonstrate that the proposed transceiver design can be considered as a MIMO broadband beamformer with constraints on the time-domain multipath length. Hence, a significant diversity gain could also be achieved by choosing strong eigenmodes of the MIMO channel. It is also found that the proposed frequency-domain methods have considerably low computational complexity as compared with their time-domain counterparts.

Multiscale theory for linear dynamic processes: Part 1. Foundations

Multiscale models of linear dynamic systems offer a representation that links states at different time scales over distinct time periods. As such they allow a natural bridging of scales (ranges of frequencies) and time, and are more attractive than models defined in the time- or frequency-domain, alone. The term “multiscale model”, as used in this two-part series, is quite different from the notion of a “multiscale model”, as this is used in recent publications, where in essence such model bridges the states of a system at two distinct scales (an atomistic scale of fast elementary phenomena, and a macroscopic scale characterizing slow continuum-based physics), described by two distinctly different physical models. The multiscale dynamic models, introduced in this paper, link state dynamics over a number of distinct time scales, and are in essence “multiresolution” facets of a single model. The outgrowth of a series of developments, which came about with the advent of the wavelet decomposition for the analysis of discrete signals, multiscale models are defined on dyadic trees, which span the time-scale space. The nodes of such trees are used to index the values of states, inputs and outputs, modeling errors, and measurement errors of dynamic systems. These values are localized in both time and scale (range of frequencies), and thus they offer a hybrid domain that is particularly conducive for estimation and control problems. In Part 1 of this series, which focuses on the foundations of a multiscale systems theory, we will describe the generation of multiscale models from their time-domain counterparts, and develop conditions governing their stability, controllability and observability. In addition, we will address the development of algorithms for the solution of basic problems, such as: optimal control, state estimation, and optimal fusion of measurements and control actions at various scales. It will be shown that multiscale models lend themselves nicely to construction of very effective parallelizable algorithms. In Part 2 of this series, we will apply all these developments to the formulation of a Multiscale Model Predictive Control (MS-MPC) approach and we will show that MS-MPC is a more attractive framework for the design and implementation of multivariable control systems.

Comparing spectra and coherences for groups of unequal size

Spectra and coherences are standard measures of association within and between time series. These measures have several advantages over their time-domain counterparts, not the least of which is the ability to derive and estimate confidence intervals. However, comparing spectra and coherences between two groups of observation is a problem that has not received much attention. This problem is important in neuroscience since it is often of great interest to determine whether the estimates differ between distinct experimental/behavioral conditions. Here we propose one approach to this problem. Based on the known distributional properties of spectral and coherence estimates, we derive a test for equality of two spectral or coherence estimates. The test is applicable to unequal sample sizes. We also derive jackknifed estimates of the variance of the proposed test statistic. We suggest that comparing the estimates obtained from the jackknife procedure with the theoretical estimates provides a robust means of determining whether the data in question shows non-Gaussian or non-stationary behavior. Finally, we present applications of the method to simulated and real data.

Symmetric spatial encoding in ultrafast 2D NMR spectroscopy

Single-scan multidimensional spectroscopy utilizes spatial dimensions for encoding the indirect-domain internal spin interactions. Various strategies have been hitherto demonstrated for fulfilling the encoding needs underlying this methodology; in analogy with their time-domain counterparts all of them have in common the fact that they proceed monotonically—starting at one end of the sample and concluding at the other. The present manuscript discusses another possibility that arises for the case of amplitude-modulated ultrafast nD NMR, whereby the spatial encoding progresses from both ends of the sample simultaneously towards the center. Such symmetric encoding is compatible with continuous or discrete excitations as well as with homonuclear or heteronuclear correlations, and exhibits a number of advantages vis-à-vis the unidirectional encodings that have been used so far: it originates echoes that are free from large first-order phase distortions, and yields nD peaks possessing a purely-absorptive character. It has the added advantage that for a given indirect-domain spectral resolution it can complete its task in half the time required by a conventional monotonic spatial encoding, leading to potentially important gains in sensitivity. The main features underlying this new spatially symmetric encoding protocol are derived, and its advantages are demonstrated with a series of amplitude-modulated homo- and hetero-nuclear 2D ultrafast NMR examples.

Data assimilative hindcast of the Gulf of Maine coastal circulation

A data assimilative model hindcast of the Gulf of Maine (GOM) coastal circulation during an 11 day field survey in early summer 2003 is presented. In situ observations include surface winds, coastal sea levels, and shelf hydrography as well as moored and shipboard acoustic Doppler D current profiler (ADCP) currents. The hindcast system consists of both forward and inverse models. The forward model is a three‐dimensional, nonlinear finite element ocean circulation model, and the inverse models are its linearized frequency domain and time domain counterparts. The model hindcast assimilates both coastal sea levels and ADCP current measurements via the inversion for the unknown sea level open boundary conditions. Model skill is evaluated by the divergence of the observed and modeled drifter trajectories. A mean drifter divergence rate (1.78 km d−1) is found, demonstrating the utility of the inverse data assimilation modeling system in the coastal ocean setting. Model hindcast also reveals complicated hydrodynamic structures and synoptic variability in the GOM coastal circulation and their influences on coastal water material property transport. The complex bottom bathymetric setting offshore of Penobscot and Casco bays is shown to be able to generate local upwelling and downwelling that may be important in local plankton dynamics.

A class of frequency-domain adaptive approaches to blind multichannel identification

We extend our previous studies on adaptive blind channel identification from the time domain into the frequency domain. A class of frequency-domain adaptive approaches, including the multichannel frequency-domain LMS (MCFLMS) and constrained/unconstrained normalized multichannel frequency-domain LMS (NMCFLMS) algorithms, are proposed. By utilizing the fast Fourier transform (FFT) and overlap-save techniques, the convolution and correlation operations that are computationally intensive when performed by the time-domain multichannel LMS (MCLMS) or multichannel Newton (MCN) methods are efficiently implemented in the frequency domain, and the MCFLMS is rigorously derived. In order to achieve independent and uniform convergence for each filter coefficient and, therefore, accelerate the overall convergence, the coefficient updates are properly normalized at each iteration, and the NMCFLMS algorithms are developed. Simulations show that the frequency-domain adaptive approaches perform as well as or better than their time-domain counterparts and the cross-relation (CR) batch method in most practical cases. It is remarkable that for a three-channel acoustic system with long impulse responses (256 taps in each channel) excited by a male speech signal, only the proposed NMCFLMS algorithm succeeds in determining a reasonably accurate channel estimate, which is good enough for applications such as time delay estimation.