Grid Of Frequencies Research Articles

Контроль электрофизических параметров метаматериалов методом поверхностных электромагнитных волн

Development of metamaterials has led to the search and choice of effective methods of radio-wave nondestructive testing of their electrophysical parameters. The existing approaches to testing based on extracted of effective electrophysical parameters of metamaterials from the coefficients of reflection and transmission of an electromagnetic wave have low reliability and don't provide their local control. We present the new radio-wave method of local control of complex dielectric permittivity and magnetic permeability, as well as the thickness of metamaterial plate on a metal substrate with surface microwaves. The method is based on the solution of inverse problem in the determination of effective electrophysical parameters of metamaterial from the frequency dependence of the attenuation coefficient of the field of a slow surface electromagnetic wave excited in a test sample. The electrophysical parameters of the metamaterial are represented as parametric frequency functions in accordance with the Drude-Lorentz models of dispersion, and the solution of the inverse problem is reduced to minimizing the objective function constructed based on the discrepancy between the experimental and design theoretical values of the attenuation coefficients of surface electromagnetic wave fields on a grid of discrete frequencies. The structure of a measuring complex that implements the proposed method of control is proposed. For the numerical and experimental verification of the method, a sample of a metamaterial plate based on SRR elements with a negative refraction region in the frequency band 10.06–10.64 GHz was investigated. Experimental investigations of the metamaterial demonstrated the theoretical capabilities gained with measurement of the local electrophysical parameters with relative error not greater 10 %.

Multifrequency optimization method of measurement the frequency dependency of electrophysical parameters of dielectric and magnetodielectric coatings

The issues of experimental determination of electrodynamic parameters of existing and new synthesized materials and coatings used in the microwave range are highlighted. Problems arising from measurements of the electrophysical and geometric parameters of dielectric and magnetodielectric coatings, taking into account their placement on a metal substrate, by radio wave methods are considered. We present the new radio wave method of joint measurements of the frequency dependence of the complex permittivity, the frequency dependence of the complex magnetic permeability, and the thickness of plane-layered samples of dielectric and magnetodielectric coatings on a metal substrate. Determination of electrophysical and geometric parameters of the coating in the proposed method is reduced to minimizing the objective function constructed based on the discrepancy between the experimental and design theoretical values of the attenuation coefficients of surface electromagnetic wave fields on a grid of discrete frequencies. The simulation model of measurements is shown, implemented on the basis of the electrodynamic modeling system CST Microwave studio (Simulia corporation, USA) and the Matlab system. The results of simulation are presented to determine the frequency dependences of the electrophysical parameters and the thickness of a sample of a radio-absorbing coating on a metal substrate. Errors in the estimates of permittivity and permeability in the measurement frequency band 9–13.5 GHz, which are no more than 10 % with a confidence level of 0.95 with a mean square deviation of the noise level of 0.006, have been obtained. The proposed method can be in demand in various science-intensive areas – microelectronic, aerospace, mechanical engineering, etc.

The frequency multiplication in electrooptical modulator of the Mach–Zehnder

The analysis of parameters of work of the electrooptical modulator of the Mach–Zehnder circuits for frequency multiplication of the radio signal. The possibilities of frequency multiplication are revealed and the optimal parameters of signals are determined. It is determined that for a given geometry of the modulator electrodes for longer laser waves, the half-wave voltage is higher than for shorter wavelengths. The maximum permissible modulation index is higher in Mach–Zehnder electrooptical modulators with a shorter wavelength of laser radiation. The number and amplitude of the spectral components at the output of the modulator depends on the amplitude of the modulating microwave signal, as well as on the location of the working point on the transfer function of the modulator. Without shifting the operating point, the Mach–Zehnder electrooptical modulator multiplies the signal frequency by 2, 4 and 6 times (to obtain even harmonics). If the modulator allows for a larger modulation index, even harmonics of a larger order can be obtained. The shift of the working point of the Mach–Zehnder modulator to the linear region of the transfer function (by half the half-wave voltage) allows to obtain odd harmonics. When the displacement voltage of the working point is equal to a quarter of the half-wave voltage, the Mach–Zehnder electrooptical modulator allows to obtain both even and odd harmonics. The maximum frequency of harmonics is limited by the allowable voltage amplitude for RF electrodes (the permissible amplitude of the modulating voltage). A further significant increase in the frequency multiplication factor is possible in circuits with two or more Mach- Zehnder modulators. Diagram with two modulators of the Mach–Zehnder allows you to get a grid of frequencies. The Mach–Zehnder modulator in the mode of odd harmonic generation can be used as a converter of sinusoidal voltage to a periodic voltage close to the pulse voltage. Radio-photon frequency multipliers have a wide band of operating frequencies. It is determined by the frequency properties of the modulator and photodetector. Frequency multipliers signal current in radiophonic systems to transfer sinusoidal frequencies in the microwave range, to synthesize a grid of frequencies.

Convolutional Beamspace for Linear Arrays

A new beamspace method for array processing, called convolutional beamspace (CBS), is proposed. It enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. But unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure and the shift-invariance are preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space. The method also generalizes to sparse arrays by effective use of the difference coarray. For this, the autocorrelation evaluated on the ULA portion of the coarray is filtered appropriately to produce the coarray CBS. It is also shown how CBS can be used in the context of sparse signal representation with dictionaries, where the dictionaries have columns that resemble steering vectors at a dense grid of frequencies. Again CBS processing with dictionaries offers better resolution, accuracy, and lower computational complexity. As only the filter responses at discrete frequencies on the dictionary grid are relevant, the problem of designing discrete-frequency FIR filters is also addressed.

Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator

Boundary Element Method frequency sweep analyses in acoustics are usually accompanied by a vast numerical cost of assembling and solving numerous linear systems. In that context, this work proposes a model order reduction technique to mitigate the resulting computational cost of such analyses. First, a series expansion of the Green’s function BEM kernel is leveraged to construct a series of frequency independent matrices. Next, in a model order reduction way, the arising matrices are projected on a reduced basis utilizing a Galerkin projection. By this off-line matrix projection, both the assembly and the solution of the BEM full-size linear systems degenerate into assembling and solving a reduced system for all frequencies. Significant speed-up factors can, thus, be achieved for both operations. The projection basis employed in this model reduction scheme is developed through an Arnoldi algorithm for the BEM systems on a grid of master frequencies. The method is based on Krylov subspaces recycling, as the subspaces produced at master frequencies are recycled to approximate the surface distribution of the acoustic variables on the whole frequency range of interest. Utilizing Krylov subspaces facilitates as well the definition of a robust error estimator that indicates the quality of the reduced system. The performance of the proposed method is assessed for both an exterior and an interior problem for a simple and more complicated geometry respectively.

Nonequidistant two-dimensional antenna arrays are based on Latin squares for registration of cosmic, atmospheric and lithospheric radiation

The possibility of using Latin squares for constructing two-dimensional non-equidistant antenna arrays that can be used for development of radio telescopes and systems for remote sensing of atmospheric and lithospheric radiation has been shown. An algorithm for calculating the coordinates of elements of a non-equidistant antenna array using the values of elements of Latin squares is proposed. It is shown that in this case, it is possible to obtain an almost complete coverage of the grid of spatial frequencies in the region of the arrangement of the elements at small filling coefficients of array. Directional patterns are studied and the side lobes levels are estimated for non-equidistant antennas obtained on the basis of Latin squares. The possibility of synthesizing of large antenna arrays on the basis of composite squares using the embedding of generative Latin squares is shown. The characteristics of the obtained arrays are studied. It is shown that using the shifts and mutual rotations of individual layers is involved in the synthesized array; its characteristics can be substantially improved.

SYSTEMATICS-INSENSITIVE PERIODIC SIGNAL SEARCH WITH K2

ABSTRACT From pulsating stars to transiting exoplanets, the search for periodic signals in K2 data, Kepler’s two-wheeled extension, is relevant to a long list of scientific goals. Systematics affecting K2 light curves due to the decreased spacecraft pointing precision inhibit the easy extraction of periodic signals from the data. We here develop a method for producing periodograms of K2 light curves that are insensitive to pointing-induced systematics; the Systematics-insensitive Periodogram (SIP). Traditional sine-fitting periodograms use a generative model to find the frequency of a sinusoid that best describes the data. We extend this principle by including systematic trends, based on a set of “eigen light curves,” following Foreman-Mackey et al., in our generative model as well as a sum of sine and cosine functions over a grid of frequencies. Using this method we are able to produce periodograms with vastly reduced systematic features. The quality of the resulting periodograms are such that we can recover acoustic oscillations in giant stars and measure stellar rotation periods without the need for any detrending. The algorithm is also applicable to the detection of other periodic phenomena such as variable stars, eclipsing binaries and short-period exoplanet candidates. The SIP code is available at https://github.com/RuthAngus/SIPK2.

The analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoid

With few exceptions, theoretical studies of periodogram properties focus on pure noise time series. This paper considers the case in which the time series consists of noise together with a single sinusoid, observed at regularly spaced time points. The distribution of the periodogram ordinates in this case is shown to be of exponentially modified Gaussian form. Simulations are used to demonstrate that if the periodogram is substantially oversampled (i.e. calculated in a dense grid of frequencies), then the distribution of the periodogram maxima can be accurately approximated by a simple form (at least at moderate signal-to-noise ratios). This result can be used to derive a calculation formula for the probability of correct signal frequency identification at given values of the time series length and (true) signal-to-noise ratio. A set of curves is presented which can be used to apply the theory to, for example, asteroseismic data. An illustrative application to Kepler data is given.

Momentum Strategies in Futures Markets and Trend-following Funds

In this paper we rigorously establish a relationship between time-series momentum strategies in futures markets and commodity trading advisors (CTAs), a subgroup of the hedge fund universe that has grown to USD 300 billion and has attracted a lot of attention during the financial crisis. Building on this relationship, we carry out the first rigorous test of the hypothesis that capacity constraints exist in trend-following investing. Using a cross-section of 71 futures contracts over the period 1974-2012, we first construct one of the most comprehensive sets of time-series momentum portfolios across various trading frequencies. Second, we provide evidence that CTAs follow time-series momentum strategies, by showing that such benchmark strategies have high explanatory power in the time-series of CTA returns. Third, based on this result, we investigate whether there exist capacity constraints in time-series momentum strategies. Consistent with the view that futures markets are relatively liquid, we do not find evidence of statistically significant capacity constraints when using two different methodologies and several robustness tests. Our results have important implications for hedge fund studies and investors. Motivated by the fact that CTA funds differ in their forecast horizons and trading activity (e.g. Hayes 2011) we extend the work of Moskowitz, Ooi and Pedersen (2012) and evaluate time-series momentum strategies in futures markets over a broad grid of lookback periods, investment horizons and frequencies of portfolio rebalancing. We find strong time-series momentum patterns in monthly, weekly

Collision-induced spectra and current astronomical research

Collision-induced spectra are the spectra of complexes of two or more atoms or molecules in a “fly-by” collisional encounter. Collision-induced absorption (CIA) has been observed in many dense gases and gas mixtures, in most cases at infrared frequencies in the form of quasi continua, and also in liquids and solids. CIA spectra of several binary complexes have been computed using modern quantum chemical methods, combined with molecular scattering theory, which couples the collisional complex to the radiation field as usual in other spectroscopic work. Binary collisional systems, such as H2 interacting with another H2 molecule, or with a helium or hydrogen atom, are first candidates for such computational work, owing to their small number of electrons and the astrophysical interest in such systems. The computed CIA spectra are found to be in close agreement with existing laboratory measurements of such spectra. Laboratory measurements exist at a limited selection of temperatures around 300 K and lower, but theory currently also provides CIA data for temperatures up to 9000 K and for higher frequencies (well into the visible), on a dense grid of temperatures and frequencies. For such calculations, detailed potential energy surfaces (PES) of the supermolecular complexes, along with the induced dipole surfaces (IDS), are needed so that the rotovibrational matrix elements of PES and IDS may be computed for the molecules involved, which may be highly rotovibrationally excited. Modern astronomical research needs opacity tables for analyses of the atmospheres of “cool” objects, such as cool white dwarfs, solar and extrasolar planets and their big moons, cool main sequence stars, and “first” stars, which are briefly described in a concluding section.

The mass of the planet-hosting giant starβGeminorum determined from its p-mode oscillation spectrum

We use precise radial velocity measurements and photometric data to derive the frequency spacing of the p-mode oscillation spectrum of the planet-hosting star Beta Gem. This spacing along with the interferometric radius for this star is used to derive an accurate stellar mass. A long time series of over 60 hours of precise stellar radial velocity measurements of Beta Gem were taken with an iodine absorption cell and the echelle spectrograph mounted on the 2m Alfred Jensch Telescope. Complementary photometric data for this star were also taken with the MOST microsatellite spanning 3.6 d. A Fourier analysis of the radial velocity data reveals the presence of up to 17 significant pulsation modes in the frequency interval 10-250 micro-Hz. Most of these fall on a grid of equally-spaced frequencies having a separation of 7.14 +/- 0.12 micro-Hz. An analysis of 3.6 days of high precision photometry taken with the MOST space telescope shows the presence of up to 16 modes, six of which are consistent with modes found in the spectral (radial velocity) data. This frequency spacing is consistent with high overtone radial pulsations; however, until the pulsation modes are identified we cannot be sure if some of these are nonradial modes or even mixed modes. The radial velocity frequency spacing along with angular diameter measurements of Beta Gem via interferometry results in a stellar mass of M = 1.91 +/- 0.09 solar masses. This value confirms the intermediate mass of the star determined using stellar evolutionary tracks. Beta Gem is confirmed to be an intermediate mass star. Stellar pulsations in giant stars along with interferometric radius measurements can provide accurate determinations of the stellar mass of planet hosting giant stars. These can also be used to calibrate stellar evolutionary tracks.

Estimation of the frequency in cyclical long-memory series

Time series with cyclical long memory are characterized by a spectral pole at some frequency ω between 0 and π such that the series has a persistent cycle of period 2π/ω, implying a quasi-periodic behaviour that slightly evolves with time. Accurate estimation of ω is needed for a precise determination of the characteristic of the series (e.g. for business cycle determination or signal estimation). We propose a simple iterative algorithm of estimation of ω based on the maximizer of the periodogram evaluated at an increasingly finer grid of frequencies and compare its performance with more usual methods of estimation restricted to Fourier frequencies. We also apply this technique to the estimation of the frequency of the sunspot index and the business cycle of the differenced unemployment level of the USA.

Interpretation of standard distortion product otoacoustic emission measurements in light of the complete parametric response.

Emission characteristics (at 2f1-f2) are measured in Mongolian gerbil as a function of the independent variation of all four stimulus parameters, the frequencies (f1 and f2) and the intensities (L1 and L2) of the two stimulus tones. The main five-dimensional display chosen is a logarithmic grid of frequencies, where for each frequency pair there is a contour map of the emission amplitude as a function of the two stimulus levels. The feature which leads to the greatest complexity in the proper interpretation of emission responses is the widespread presence of "notches" in these contour maps. Notches are lines of relative minima in the emission amplitude, and are found at either: (1) constant L1, but only in regions where L1 > L2; or (2) at constant L2, only where L2 > or = L1. Notches are not found at any other orientations, and are associated with emission phase shifts of about 180 degrees as the notch line is traversed. These notch characteristics are explained by phase cancellation in a simple cochlear amplifier model in which there is a change, as a function of the stimulus level alone, of relevant characteristics of the cochlear response to a single tone. Only one mechanism of emission generation is required to explain the observed patterns, i.e., there is no need to invoke different "active" and "passive" mechanisms. Unless properly accounted for, the presence of notches adversely affects all of the standard emission measurements, i.e., all methods which cover a restricted parameter set such as DPgrams, input-output or "growth" functions, and frequency ratio functions. Conversely, because the notch location appears approximately invariant in the cochlea, notches potentially make it possible to use certain emission growth functions to estimate forward and reverse middle-ear transfer functions.

Sounding the magnetosphere by signals from VLF radio transmitters

Abstract A new remote sensing method for the Earth's magnetosphere is suggested. The method is based on the parametric reflection of whistler mode waves from the level in the magnetosphere where a whistler wave frequency coincides with the local lower hybrid resonance frequency. In this region a sufficiently intense whistler signal generates two electrostatic plasma waves which can produce a reflected whistler wave. The known localization of the whistler reflection leads us to suggest a new method of electron density measurements in the magnetosphere, using a grid of frequencies from a powerful ground-based VLF transmitter. Parametric reflection of whistler signals in the magnetosphere can appear from naturally occurring short-scale low frequency turbulence (ion sound or ion cyclotron waves). In this case, using this new method we can obtain important information about this turbulence. Some experimental data which demonstrate the appearance of VLF echo signals from the magnetosphere with anomalously small group time delays are discussed from this point of view.

Hyperfine Interactions in the ν 3 Band of Osmium Tetroxide: Accurate Determination of the Spin-Rotation Constant by Crossover Resonance Spectroscopy

A series of three papers is devoted to a detailed presentation of the hyperfine interactions in the ν 3 band of OsO 4. In this first paper, we emphasize the experimental aspects although a first theoretical approach of the hyperfine problem is given. Several recording techniques with a resolution of about 1 kHz have enabled us to measure very precisely a set of hyperfine structures of 189OsO 4 and 187OsO 4. The oservation crossover resonances, with high- J values, gave access to an independent determination of the hyperfine structures in the lower and upper levels. As a consequence, hyperfine constants are determined very accurately. This is illustrated by the determination of the spin-rotation constant of the two isotopic species: c a ( 189OsO 4) = −21.6891(33) kHz and c a ( 187OsO 4) = −6.379(20) kHz, and the isotopic relation is verified with a relative precision of 3 × 10 −3. In addition, we report a grid of absolute frequencies of 70 fundamental lines with an accuracy ranging from 50 Hz to 2 kHz.

Identification in ℋ∞ with nonuniformly spaced frequency response measurements

In this paper, the problem of ‘system identification in ℋ∞’ is investigated in the case when the given frequency response data are not necessarily on a uniformly spaced grid of frequencies. A large class of robustly convergent identification algorithms is derived. A particular algorithm is further examined and explicit worst case error bounds (in the ℋ∞ norm) are derived for both discrete-time and continuous-time systems. An example is provided to illustrate the application of the algorithms.

FITTING SPATIAL CORRELATION MODELS: APPROXIMATING A LIKELIHOOD APPROXIMATION

Summary The paper considers a class of spatial correlation models (stationary Gaussian processes) which includes (spatial) conditional autoregressive, simultaneous autoregressive, moving average and direct covariance models. Given observations on a finite rectangular lattice, a likelihood approximation for estimating the parameters in the spectral density of the model is discussed. The approximation consists of applying the trapezoidal rule, with a her grid of frequencies than the usual Fourier frequencies, to compute the integral in an appraximation due to Whittle (1954) and later modified by Guyon (1984). With this approximation, a Fisher scoring type algorithm has a simple form and in some casea reduces to iteratively reweighted least squares. Methods for computing the unbiased two-dimensional periodogram required by the method are presented and the accuracy of the approximation is discussed. The asymptotic distribution of the parameter estimates computed from the likelihood approximation is also given.

On computing the infinity norm

An iterative algorithm is given for computing the infinity norm of the transfer matrix of a bounded, linear, time-invariant, finite-dimensional system. The procedure, which is based on the numerically stable QZ algorithm, enables the infinite norm to be computed with a guaranteed accuracy. No ad hoc procedures, such as those for selecting a suitable grid of frequencies, for example, are used. The degree of accuracy is under the direct control of the user, with each additional decimal place of accuracy requiring approximately=3.3 calls to the QZ algorithm. Experience has shown the algorithm to function reliably and in reasonable time for models of order as large as 56.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast computation of finger-length-weighted SAW transducer dynamic admittance

A formula for the dynamic admittance of a finger-length-weighted transducer with uniform periodicity and duty factor is derived. Subsequent transformation of the formula makes computation of transducer dynamic admittance on the grid of frequencies extremely fast.

Towards a new absolute frequency reference grid in the 28 THz range

We present a grid of absolute reference frequencies based on CO2 (or N2O) lasers locked to saturation peaks of heavy molecules. Frequency differences between OsO4 peaks corresponding to adjacent CO2 laser lines from P(12) to P(22) have been measured with 1 kHz accuracy. This set includes one 192OsO4 resonance whose absolute frequency is known with the same accuracy. This absolute grid is then used to provide an absolute calibration of the ν3 band saturation spectrum of SF6. We also find a 23 kHz average frequency difference between the CO2 grid and the new OsO4 grid which we interpret tentatively as a small extrapolation error from the R to the P branch frequencies of CO2.