Time Interpolation Research Articles

Time-Interval Measurement Based on SAW Filter Excitation

This paper deals with a novel time-interval measurement method that makes use of a surface acoustic wave (SAW) filter as a time interpolator. The method is based on the fact that a transversal SAW filter excited by a short pulse can generate a well-defined finite signal with highly suppressed spectra outside a narrow frequency band. If the responses to two excitations are sampled at clock ticks, they can be precisely reconstructed from a finite number of samples and then compared to determine the time interval between the two excitations. As a first step of a more comprehensive discussion of the method, the time-interpolation error caused by deterministic effects has been analyzed in this paper. It has been shown that the mean square of the interpolation error is limited by the upper bound, which is proportional to the relative energy of aliasing distortion and inversely proportional to the square of the filter center frequency. The upper bound has been compared to the results obtained from the simulation based on a linear-phase transversal filter. The RMS error resulting from the simulation exactly follows the slope of the theoretical upper bound, and it is approximately four times smaller than that. The described method excels in time interpolation efficiency since the time interpolation error relative to clock period is small; in other words, accurate measurement can be achieved even with a relatively low clock frequency. This has been practically demonstrated in a time-interval counter, which provides precision of 7-ps RMS using a clock frequency as low as 16.4 MHz. It results from the analysis that using state-of-the-art elements in the interpolator, the deterministic interpolation error on the order of 0.1 ps can be achieved.

View and Time Interpolation in Image Space

AbstractThe ability to interpolate between images taken at different time and viewpoints directly in image space opens up new possiblities. The goal of our work is to create plausible in‐between images in real time without the need for an intermediate 3D reconstruction. This enables us to also interpolate between images recorded with uncalibrated and unsynchronized cameras. In our approach we use a novel discontiniuity preserving image deformation model to robustly estimate dense correspondences based on local homographies. Once correspondences have been computed we are able to render plausible in‐between images in real time while properly handling occlusions. We discuss the relation of our approach to human motion perception and other image interpolation techniques.

Adaptive Concurrent Equalization Applied to Multicarrier OFDM Systems

Receivers for wireless Orthogonal Frequency Division Multiplexing (OFDM) systems usually perform the channel estimation based on pilot carriers in known positions of the channel spectrum. Interpolation is applied between pilot carriers to determine the channel transfer function in all carrier frequencies. Channel variations along time are compensated by means of interpolation between successive channel estimates on the same carrier frequency. However, not rarely do fast channel variations exceed the time interpolator capability, as is the case for mobile operation. In this article we propose a new technique based on concurrent de- convolution, as a mean to further increase the time interpolator capability. Concurrent deconvolution, also known as concurrent equalization, is based on the concurrent operation of two stochastic gradient time-domain algorithms. One gradient-based algorithm minimizes a cost function that measures the received signal energy dispersion and the other minimizes the Euclidean distance between the received digital modulation symbols and the ones in the reference constellation which are assigned to each OFDM sub-channel. Results show that the proposed technique, when subsequently applied to the time interpolation stage, improves the system robustness for fast varying channels. The whole channel compensation computational cost is increased by the cost of a two coefficient multirate adaptive FIR filter, added only to those subcarriers at the FFT output to which a pilot sequence has not been assigned.

Lagrangian Finite–Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy

A new finite element scheme for the numerical simulation of three-dimensional time-dependent flow of viscoelastic fluids is presented. The viscoelastic fluids are of the K-BKZ integral type and the method is based on a Lagrangian kinematics description of the fluid flow. The spatial coordinate system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme converges with respect to discretization of the spatial and time dimensions, both with third order.

Primary productivity and export fluxes on the Canadian shelf of the Beaufort Sea: A modelling study

We present a coupled sea ice–ocean-biological (including ice algae) model in the Arctic Ocean. The 1D model was developed and implemented on the Canadian Beaufort Sea shelf to examine the importance of different physical processes in controlling the timing and magnitude of primary production and biogenic particle export over an annual cycle (1987). Our results show that the snow and sea ice cover melt and/or break-up controls the timing of the phytoplankton bloom but primary producers (ice algae and phytoplankton) on the outer shelf are essentially nutrient limited. The total annual primary production (22.7 to 27.7 g-C m − 2 ) is thus controlled by nutrient “pre-conditioning” in the previous fall and winter and by the depth of wind mixing that is controlled in part by the supply of fresh water at the end of spring (ice melt or runoff). The spring bloom represents about 40% of the total annual primary production and occurs in a period of the year when sampling is often lacking. Time interpolation of observed values to obtain total annual primary production, as done in many studies, was shown to lead to an underestimation of the actual production. Our simulated ratios of export to primary production vary between 0.42 and 0.44.

Random Errors in Time Interval Measurement Based on SAW Filter Excitation

This paper deals with the time interval measurement method that makes use of a surface acoustic wave (SAW) filter as a time interpolator. The method is based on the fact that a transversal SAW filter excited by a short pulse can generate a finite signal with highly suppressed spectra outside a narrow frequency band. If the responses to two excitations are sampled at clock ticks, they can be precisely reconstructed from a finite number of samples and then compared to determine the time interval between the two excitations. We have analyzed noise contributions to the overall uncertainty of the interval measurement. The following four noise sources have been considered: (1) noise of excitation; (2) noise of amplifier; (3) quantization noise of the analog-to-digital converter; and (4) clock and sampling jitter. The main goal of the analysis was to determine the uncertainty of the measurement in dependence on the variances of contributing noises, and the magnitude of the frequency response of the filter. First, each uncertainty component has been analyzed under general assumptions. Second, a general narrow-band filter has been investigated. Finally, we have found the solution for an ideal narrow-band filter where we have obtained simple illustrative results. The results have been compared to Monte-Carlo simulations. Good agreement between theory and simulation has been demonstrated except for the outliers due to the false ambiguity solution that occurs with large measurement errors and small relative filter bandwidth.

Simultaneous nearby measurements of acoustic propagation and high‐resolution sound speed structure containing internal waves

On two occasions during the SW06 experiment, towed CTD chain measurements were made close to an acoustic propagation path. The acoustic path was 1 km long, oriented roughly in the direction of propagation of large nonlinear internal waves. On the first occasion, large nonlinear internal waves were absent, and on the second occasion, they were present. The CTD chain was towed in loops around the acoustic path, roughly 200 m on either side of the path. On the first occasion, 17 loops were made in about 5.5 hr, and on the second occasion, 7 loops were made in about 2.5 hr. Throughout these time periods, acoustic transmissions between 2 kHz and 10 kHz were carried out. The acoustic environment on the path is estimated by space and time interpolation between the tows on the two sides of the path. The acoustic data is compared with propagation modeling in this environment.

Variational r‐adaption in elastodynamics

AbstractWe develop a variational r‐adaptive finite element framework for solid dynamic applications and explore its conceptual links with the theory of dynamic configurational forces. The central idea underlying the proposed approach is to allow Hamilton's principle of stationary action to determine jointly the evolution of the displacement field and the discretization of the reference configuration of the body. This is accomplished by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously. However, we find that a naive consistent Galerkin discretization of the action leads to intrinsically unstable solutions. Remarkably, we also find that this unstable behavior is eliminated when a mixed, multifield version of Hamilton's principle is adopted. Additional features of the proposed numerical implementation include the use of uncoupled space and time discretizations; the use of independent space interpolations for velocities and deformations; the application of these interpolations over a continuously varying adaptive mesh; and the application of mixed variational integrators with independent time interpolations for velocities and nodal parameters. The accuracy, robustness and versatility of the approach are assessed and demonstrated by way of convergence tests and selected examples. Copyright © 2007 John Wiley & Sons, Ltd.

An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes - V. Local time stepping andp-adaptivity

SUMMARY This article describes the extension of the arbitrary high-order Discontinuous Galerkin (ADER-DG) method to treat locally varying polynomial degress of the basis functions, so-called p-adaptivity, as well as locally varying time steps that may be different from one element to another. The p-adaptive version of the scheme is useful in complex 3-D models with small-scale features which have to be meshed with reasonably small elements to capture the necessary geometrical details of interest. Using a constant high polynomial degree of the basis functions in the whole computational domain can lead to an unreasonably high CPU effort since good spatial resolution at the surface may be already obtained by the fine mesh. Therefore, it can be more adequate in some cases to use a lower order method in the small elements to reduce the CPU effort without loosing much accuracy. To further increase computational efficiency, we present a new local time stepping (LTS) algorithm. For usual explicit time stepping schemes the element with the smallest time step resulting from the stability criterion of the method will dictate its time step to all the other elements of the computational domain. In contrast, by using local time stepping, each element can use its optimal time step given by the local stability condition. Our proposed LTS algorithm for ADER-DG is very general and does not need any temporal synchronization between the elements. Due to the ADER approach, accurate time interpolation is automatically provided at the element interfaces such that the computational overhead is very small and such that the method maintains the uniform high order of accuracy in space and time as in the usual ADER-DG schemes with a globally constant time step. However, the LTS ADER-DG method is computationally much more efficient for problems with strongly varying element size or material parameters since it allows to reduce the total number of element updates considerably. This holds especially for unstructured tetrahedral meshes that contain strongly degenerate elements, so-called slivers. We show numerical convergence results and CPU times for LTS ADER-DG schemes up to sixth order in space and time on irregular tetrahedral meshes containing elements of very different size and also on tetrahedral meshes containing slivers. Further validation of the algorithm is provided by results obtained for the layer over half-space (LOH.1) benchmark problem proposed by the Pacific Earthquake Engineering Research Center. Finally, we present a realistic application on earthquake modelling and ground motion prediction for the alpine valley of Grenoble.

Time interval measurement device based on surface acoustic wave filter excitation, providing 1ps precision and stability

This article deals with the time interval measurement device, which is based on a surface acoustic wave (SAW) filter as a time interpolator. The operating principle is based on the fact that a transversal SAW filter excited by a short pulse can generate a finite signal with highly suppressed spectra outside a narrow frequency band. If the responses to two excitations are sampled at clock ticks, they can be precisely reconstructed from a finite number of samples and then compared so as to determine the time interval between the two excitations. We have designed and constructed a two-channel time interval measurement device which allows independent timing of two events and evaluation of the time interval between them. The device has been constructed using commercially available components. The experimental results proved the concept. We have assessed the single-shot time interval measurement precision of 1.3 ps rms that corresponds to the time of arrival precision of 0.9 ps rms in each channel. The temperature drift of the measured time interval on temperature is lower than 0.5 ps/K, and the long term stability is better than +/-0.2 ps/h. These are to our knowledge the best values reported for the time interval measurement device. The results are in good agreement with the error budget based on the theoretical analysis.

The Variational Assimilation Method for the Retrieval of Humidity Profiles with the Wind-Profiling Radar

Abstract Recently, a humidity estimation technique was developed by using the turbulence echo characteristics detected with a wind-profiling radar. This study is concerned with improvement of the retrieval algorithm for delineating a humidity profile from the refractive index gradient (M) inferred from the echo power. To achieve a more precise estimate of humidity, a one-dimensional variational method is adopted. Because the radar data provide only the absolute value of M, its sign must be determined in the retrieval. A statistical probability for the sign of M [Pr(z)] is introduced to the cost function of the variational method to determine the optimum result with reduced calculation cost. GPS-derived integrated water vapor (IWV) was assimilated together with the radar-derived |M| for constraining the signs of |M| to agree with the radar-derived IWV and the GPS-derived IWV. Humidity profiles were retrieved from the Middle and Upper Atmosphere (MU) radar–Radio Acoustic Sounding System (RASS) data for July–August 1999 using the first guess calculated from the time interpolation of radiosonde results. The |M| profiles from the MU radar–RASS were assimilated at 21 height layers between 1.5 and 7.5 km. A genetic algorithm is employed to find the global optimum. The humidity profiles are retrieved with the same vertical resolution as that of the observation values. The precision of the retrieval result using the new method is superior to that of the conventional method. The difference between the analysis and simultaneous radiosonde results was related to a large error in the first guess. The sensitivity of the analysis result to the shape of the Pr(z) profile was investigated, and the result appears to be insensitive to the profile of Pr(z). The improvement over the conventional method is especially evident for the case of a large error in the first guess.

Frequency domain concurrent channel equalization for multicarrier systems

Receivers for wireless Orthogonal Frequency Division Multiplexing (OFDM) systems usually perform the channel estimation based on pilot carriers in known positions of the channel spectrum. Interpolation between pilot carriers is applied to determine the channel transfer function in all carrier frequencies. Channel variations along time are compensated by means of interpolation between successive channel estimates on the same carrier frequency. However, not rarely, the fast channel variations exceed the time interpolator capability, as is the case for mobile operation. In this article we present a new channel compensation technique based on the concurrent operation of two stochastic gradient time-domain algorithms, one which minimizes a cost function that measures the received signal energy dispersion and other which minimizes the Euclidean distance between the received digital modulation symbols and the ones in the reference constellation assigned to each OFDM sub-channel. Results show that the new technique advantageously improves the system robustness to fast channel variations since, with a low computational cost, it dramatically reduces the demodulator symbol error rate even when the receiver is operating in an intense dynamic multipath scenario.

Frequency domain concurrent channel equalization for multicarrier systems

Abstract Receivers for wireless Orthogonal Frequency Division Multiplexing (OFDM) systems usually perform the channel estimation based on pilot carriers in known positions of the channel spectrum. Interpolation between pilot carriers is applied to determine the channel transfer function in all carrier frequencies. Channel variations along time are compensated by means of interpolation between successive channel estimates on the same carrier frequency. However, not rarely, the fast channel variations exceed the time interpolator capability, as is the case for mobile operation. In this article we present a new channel compensation technique based on the concurrent operation of two stochastic gradient timedomain algorithms, one which minimizes a cost function that measures the received signal energy dispersion and other which minimizes the Euclidean distance between the received digital modulation symbols and the ones in the reference constellation assigned to each OFDM sub-channel. Results show that the new technique advantageously improves the system robustness to fast channel variations since, with a low computational cost, it dramatically reduces the demodulator symbol error rate even when the receiver is operating in an intense dynamic multipath scenario.

A stabilized finite element model for the hydrothermodynamical simulation of the Rio de Janeiro coastal ocean

AbstractIn this paper, a stabilized space–time Petrov–Galerkin finite element model of coastal ocean circulation is derived. Continuous linear interpolation in space and time is employed and a spatial unstructured mesh of triangular elements is used. To simulate the hydro‐thermodynamical ocean behaviour a gravity reduced model is proposed. This model solves the motion and continuity hydrodynamic equations coupled with the advection–diffusion transport equation for temperature which governs the heat exchanges in the upper layer. The model is used to evaluate the main dynamical features of the coastal waters of the Rio de Janeiro State, namely: cold plumes, coastal jets and the influence of the warmer water bays. Numerical experiments are performed to highlight the typical observed events of coastal upwelling phenomena and their interaction with the existing coastal bays and the offshore conditions. Such experiments deal with a series of idealized northeast wind field forcing patterns, showing the solutions dependence on the horizontal structure of the wind fields in relation to the coastline configuration. Copyright © 2007 John Wiley & Sons, Ltd.

The inadequacy of monitoring without modelling support

There is much to gain in joining monitoring and modelling efforts, especially in the present process of implementing the European Water Framework Directive and in the coming implementation of the Groundwater Directive. Nevertheless, present practises in the water management world suggest that most often models are not considered an option when monitoring obligations in the WFD are solved. The present paper analyses the constraints, such as perceived insufficiency of data for modelling, lack of explicit requirement for modelling in the WFD and its associated technical guidance documents, lack of awareness about what models can do and lack of confidence in models by water managers and policy makers. The findings have mainly emerged from a series of Harmoni-CA workshops aiming at bringing the monitoring and modelling communities together for a discussion of benefits and constraints in the joint use of monitoring and modelling. The workshops were attended by scientists, water managers, policy makers, stakeholders and consultants. The overall conclusion is that modelling can significantly improve the benefits of monitoring data; by quality assurance of data, interpolation and extrapolation in space and time, development of process understanding (conceptual models), and the assessment of impacts of pressures and effects of programmes of measures.

A comparison between anisotropic reverse time and phase-shift plus interpolation prestack migrations for tilted anisotropic media

Two 2D anisotropic prestack depth migration algorithms that use wavefield extrapolation are evaluated for tilted transversely isotropic media (TTI). The first method is anisotropic phase-shift-plus-interpolation (A-PSPI) that is based on an analytical solution of frequency-dispersion enabling the use of an arbitrary distribution of velocities and anisotropic parameters. The second method is anisotropic reverse-time (A-RT) that uses the full wave equation. we evaluate the accuracy and efficiency of there algorithms. Examples are presented that use numerica and physically modelled data along with a structurally complex real data example. Both A-PSPI and A-RT have excellent performance with A-RT maintaining the advantage of using the full wave equation.

A Time-Domain Iteration Method for Acoustic Scattering Problems

This paper presents a new time-domain iteration method for computing multifrequency scattering waves from underwater obstacles. The equations are expressed in some forms relative to the retarded time, and the solution of scattering potential can be computed by an iteration process in which the boundary condition on each panel is naturally satisfied. Thus, the present method can treat the scattering problem of geometries with multiple sharp edges. In addition, the numerical inaccuracy due to time interpolation is minimized by using a Fourier series, and the results can robustly converge to correct values by setting zero initial scattering potentials. Several cases of a half sphere in different frequency ranges and one of multifrequency were tested by the present method. The results of all these cases agree with those reached by a frequency-domain boundary element method (BEM). In addition, a case with multiple sharp edges is also tested. The converged results can be obtained by the present method, but not by the BEM. Moreover, the present method is more computationally efficient, especially for the multifrequency case.

Key aspects of stratospheric tracer modeling using assimilated winds

Abstract. This study describes key aspects of global chemistry-transport models and their impact on stratospheric tracer transport. We concentrate on global models that use assimilated winds from numerical weather predictions, but the results also apply to tracer transport in general circulation models. We examined grid resolution, numerical diffusion, air parcel dispersion, the wind or mass flux update frequency, and time interpolation. The evaluation is performed with assimilated meteorology from the "operational analyses or operational data" (OD) from the European Centre for Medium-Range Weather Forecasts (ECMWF). We also show the effect of the mass flux update frequency using the ECMWF 40-year re-analyses (ERA40). We applied the three-dimensional chemistry-transport Tracer Model version 5 (TM5) and a trajectory model and performed several diagnoses focusing on different transport regimes. Covering different time and spatial scales, we examined (1) polar vortex dynamics during the Arctic winter, (2) the large-scale stratospheric meridional circulation, and (3) air parcel dispersion in the tropical lower stratosphere. Tracer distributions inside the Arctic polar vortex show considerably worse agreement with observations when the model grid resolution in the polar region is reduced to avoid numerical instability. The results are sensitive to the diffusivity of the advection. Nevertheless, the use of a computational cheaper but diffusive advection scheme is feasible for tracer transport when the horizontal grid resolution is equal or smaller than 1 degree. The use of time interpolated winds improves the tracer distributions, particularly in the middle and upper stratosphere. Considerable improvement is found both in the large-scale tracer distribution and in the polar regions when the update frequency of the assimilated winds is increased from 6 to 3 h. It considerably reduces the vertical dispersion of air parcels in the tropical lower stratosphere. Strong horizontal dispersion is not necessarily an indication of poor wind quality, as observations indicate. Moreover, the generally applied air parcel dispersion calculations should be interpreted with care, given the strong sensitivity of dispersion with altitude. The results in this study provide a guideline for stratospheric tracer modeling using assimilated winds. They further demonstrate significant progress in the use of assimilated meteorology in chemistry-transport models, relevant for both short- and long-term integrations.

Numerical implementation of fundamental solution for solving 2D transient poroelastodynamic problems

This paper presents the numerical implementation of boundary element formulation for solving two-dimensional poroelastodynamic problems in time domain. The derivation of the time-dependent integral equations is based on the Biot’s theory and the reciprocal theorem. The analytical form of a 2D fundamental solution in time domain for porous media with incompressible components (solid particles and fluid) is derived and validated. After the analytical time integration of the fundamental solution kernels, a time-marching procedure is established. The comparison of different time interpolation functions shows that the mixed interpolation gives more stable response. In addition, the linear θ method is used in order to improve the numerical stability of the proposed approach. Finally, two examples are presented to investigate the stability and the accuracy of this approach for wave propagation analyses.

A Low-Cost Low-Power CMOS Time-to-Digital Converter Based on Pulse Stretching

A low-cost and low-power CMOS time-to-digital converter (TDC) with 50-ps time resolution is proposed in this paper. The reference clock frequency of the TDC is 80 MHz and the input range is theoretically unlimited. Two parallel time interpolators are used to improve the resolution by pulse stretching. In addition to conventional current ratio and capacitor ratio, the duty cycle of the discharging clock is also incorporated to adjust the stretch factor to reduce the power consumption and chip area dramatically. The interpolators are based on analog dual-slope conversion. The time resolution is measured as 50 ps and the integral nonlinearity (INL) error is within plusmn1.1 LSB for input range up to 250ns. The temperature drift of the measured resolution is -15.2% to +13% over a temperature range of -40degC to 80degC, which is significantly smaller than plusmn125% drift over 100degC temperature range in previous work. The voltage drift is 3.8 ps/V or equivalently plusmn3.5% over 3.0-4.0 V supply voltage range. The measured resolution is within 49.8 ps to 52.7 ps for six packaged chips and the chip size is merely 0.5 mmtimes0.45mm as fabricated in the TSMC 0.35-mum CMOS digital process. The power consumption is 0.75mW, enormously reduced from hundreds of milliwatts of the predecessors, at 100 k samples/s and the measurement rate can achieve as high as 150 k samples/s