Frequency Space Analysis Research Articles

Quantum gravitational sensor for space debris

Matter-wave interferometers have fundamental applications for gravity experiments such as testing the equivalence principle and the quantum nature of gravity. In addition, matter-wave interferometers can be used as quantum sensors to measure the local gravitational acceleration caused by external massive moving objects, thus lending itself for technological applications. In this paper, we will establish a three dimensional model to describe the gravity gradient signal from an external moving object, and theoretically investigate the achievable sensitivities using the matter-wave interferometer based on the Stern-Gerlach set-up. As an application we will consider the Mesoscopic Interference for Metric and Curvature (MIMAC) and Gravitational wave detection scheme [New J. Phys. 22, 083012 (2020)] and quantify its sensitivity to gravity gradients using frequency-space analysis. We will consider objects near Earth-based experiments and space debris in proximity of satellites and estimate the minimum detectable mass of the object as a function of their distance, velocity, and orientation.

IRlab - Platform for thermal video analysis in evaluation of peripheral thermal behavior and blood perfusion

Background and objectivesDynamic thermal imaging in medicine has several advantages in comparison to static thermal image analysis and has potential as a novel patient assessment method e.g. in the area of vascular surgery. Since dynamic thermal imaging has become in the scope of research only during the last decade, the computational available analysis methods are often lacking or not existing. Most of the published software is not available to the research community or are behind a paywall. IRlab provides an easy-to-use dynamic thermal video processing and analysis platform, freely accessible to researchers. MethodsIRlab is programmed in Matlab R2020b. Computational tools for dynamic analysis are divided into spatio-temporal and spectral methods, where spatio-temporal methods consist of region of interest delineation tools, thermal modulation analysis, standard thermal measures such as median, maximum, minimum and deviation values, and subtraction and gamma maps. Spectral methods include spectral band power, spectral flow, and wavelet analysis tools. Preliminary data of a single healthy subject was analyzed with the program as a sample run. ResultsIRlab provides a platform for lower limb thermal image and video analysis with a clear workflow and variety of processing and analysis tools for time and frequency space analysis. The whole source code for IRlab is freely available for the research community under the General public license. ConclusionsIRlab is a versatile tool for dynamic thermal image and video processing. Freeware and open-source programs for medical thermal imaging are severely lacking, thus as a completely open-source project IRlab offers a unique platform for researchers within the field of medical thermal imaging.

Detection and Removal of Periodic Noise in Kepler/K2 Photometry with Principal Component Analysis

Abstract We present a novel method for detrending systematic noise from time series data using Principal Component Analysis (PCA) in Fast Fourier Transforms. This method is demonstrated on time series data obtained from the inaugural campaign of the Kepler K2 mission, as well as three objects of interest from Campaign 4. Unlike previous detrending techniques that utilize PCA, this method performs the detrending in Fourier space rather than temporal space. The advantage of performing the analysis in frequency space is that the technique is sensitive purely to the periodicity of the unwanted signal and not to its morphological characteristics. This method could improve measurements of low signal-to-noise photometric features by reducing systematics. We also discuss challenges and limitations associated with this technique.

Dynamic monitoring of glycine crystallisation with low power ultrasound reflection spectroscopy

Crystallisation processes are ubiquitous in the food and pharmaceutical industries and the development of process analytical technologies (PAT) for on-line, in situ monitoring is essential to ensure process efficiency and to optimise product quality. Current PAT, many of which are based on electromagnetic waves, have a range of limitations including an inability to accurately measure opaque solutions. Low power (<10Wm−2) pulsed acoustic techniques, such as ultrasound reflectance and velocimetry, have the benefit of being non-material altering, affordable, non-invasive and can study opaque systems without any dilution. Here, we present an improved in-situ ultrasound technique which is corroborated with optical turbidity in the measurement of the MSZW of glycine in water with good agreement. A Mann–Whitney U test was conducted, and no significant difference was found in the measurement of the MSZW between the two techniques. Density data were used with velocity measurements from the improved technique to calculate adiabatic compressibility of glycine solutions, which is an important and useful physical property when studying phase transitions. A frequency space analysis has been performed on the acoustic time domain measurements, and the data suggest the presence of scattering bodies in the metastable zone.

Note: Derivative divide, a method for the analysis of broadband ferromagnetic resonance in the frequency domain.

Broadband ferromagnetic resonance (bbFMR) spectroscopy is an established experimental tool to quantify magnetic properties. Due to frequency-dependent transmission of the microwave setup, bbFMR measurements in the frequency domain require a suitable background removal method. Here, we present a measurement and data analysis protocol that allows us to perform quantitative frequency-swept bbFMR measurements without the need for a calibration of the microwave setup. We furthermore compare the results of the proposed frequency space analysis and a conventional analysis in field-space of bbFMR data obtained from a permalloy thin film. The very good agreement of the extracted parameters using the two methods shows the reliability of our method.

A Pilot Study Based on Cerebral Hemoglobin Information to Classify the Desired Walking Speed

To achieve more intelligent performance for walking-assistive devices, spontaneous motion intention of walking speed should be identified for providing a control command. In this letter, cerebral hemoglobin information was analyzed to recognize three levels of walking speed: low, medium, and high speed. Thirty subjects performed walking tasks in three levels of speed, with cerebral hemoglobin information being recorded and oxygenated hemoglobin (oxyHb) mainly analyzed. A novel method of time–frequency–space analysis is proposed to extract features through two steps. First, a wavelet packet method is used to analyze the oxyHb signals in four frequency bands [(I) 0–0.03 Hz, (II) 0.03–0.06 Hz, (III) 0.06–0.09 Hz, and (IV) 0.09–0.12 Hz]. Second, spatial features were summarized for each frequency band. The support vector machine method is used to identify speed levels. The dataset of 15 people is used to train the model, and the dataset of the other 15 people is used for validation. The final recognition rates of low, medium, and high speed are 93.33%, 66.67%, and 80%, respectively. The average recognition is up to 80%. The results indicate that the proposed method of time–frequency–space analysis is feasible for recognizing expected walking speed, and cerebral hemoglobin information could reflect humans’ spontaneous motion intention. Moreover, it may provide a more intelligent control method for walking-assistive devices and promote its development in the future.

Resting Heart Rate Variability, Inflammation, and Insulin Resistance in Overweight and Obese Adolescents.

The prevalence of obesity is increasing in young people in the United States. Lately, low-grade inflammation is recognized as accompanying obesity, a known risk factor for type 2 diabetes. Autonomic dysfunction is a prominent feature of adult diabetes, but its prevalence in adolescents in prediabetic states or with diabetes risk factors is unknown. We undertook to study obesity, inflammation, insulin resistance, and autonomic dysfunction together in a population of adolescents aged 13-18 years. Subjects gave a blood sample for cytokine analysis and a 5-min resting EKG for analysis of resting heart rate variability. TNF-α, IL-6, c-reactive protein (CRP), MCP-1, and IL-10 were analyzed by enzyme-linked immunosorbent assay, and Fourier Transform was applied to electrocardiographic recordings of R-R intervals for analysis in frequency space. The HOMA calculation was used as an index of insulin sensitivity. TNF-α, IL-6, CRP, MCP-1, HOMA, and insulin levels, but not serum glucose or IL-10, were higher in the obese subjects. Low-frequency (0.04-0.15 Hz) and high-frequency (0.15-0.4 Hz) fluctuations of R-R intervals were lower in the obese subjects, but the normalized low-frequency power was not different, suggesting proportional reduction in variability in both ranges and impairment of both sympathetic and parasympathetic systems. Chronic low-grade inflammation, insulin resistance, and autonomic dysfunction are present at an early age in obese youths; early detection of inflammation may facilitate meaningful lifestyle changes in this high-risk group.

Time decay and exponential stability of solutions to the periodic 3D Navier–Stokes equation in critical spaces

Using analysis in frequency space and Fourier methods, we establish that the global solution to the three‐dimensional incompressible periodic Navier–Stokes equation for initial data in the critical Sobolev space decays exponentially fast to zero, and it is exponentially stable as time goes to infinity as soon as the initial data (hence the solution) are mean free; otherwise, the difference to the average does so. Furthermore, we prove that any global nonmean‐free solution vanishes as time goes to infinity, and it is globally exponentially stable. The main tools are the energy methods, the Friedrich's approximating schema, and a crucial change of function that depends explicitly on time. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Improving the signal-to-noise ratio of the visual P300

The P3b (“P300”) [1] of the event-related potential is considered to reflect cognitive —or even conscious [2]— stimulus processing. P300 recording sessions employ an “oddball paradigm”: target stimuli appear only infrequently among non-target stimuli. Thus they are quite lengthy and difficult to use with patients. We tested different strategies for minimizing the time needed to record a reliable visual P300. Targets were gratings of different orientation for target and non-target stimuli. Since previous studies only assessed absolute amplitude [e.g., 3, 4], we first determined the optimal signal-to-noise ratio for different target infrequencies. We found target-to-non-target ratios of 1:4 to 1:8 to be optimal. We next assessed whether shrinking the interval between stimulus onsets from 1000 ms to 214 ms would improve the signal-to-noise ratio when the recording time is kept constant, despite a temporal overlap of responses. This was indeed the case by a margin of up to 60%, but depended on the presentation duration of the stimuli. Finally, we assessed whether it is feasible to record a P300 in a manner similar to a steady-state visual evoked potential with a fixed number of intervening non-targets. We found a high inter-individual variability, but could reliably identify responses in all subjects with a multi-harmonic frequency-space analysis. Compared to conventional P300 recordings, less recording time was needed to acquire significant responses. In conclusion, the signal-to-noise ratio and the efficiency of visual P300 recordings can be improved by choosing optimal target infrequencies and by employing rapid stimulation schemes. [1] Linden, D. E. J. (2005). Neuroscientist 11:563-576. [2] Kotchoubey, B. (2005). Progr Brain Res 150:427-444. [3] Johnson, Jr. R. (1986). Psychophysiology 23:367-384. [4] Polich, J., & Margala, C. (1997). Int J Psychophysiol 25:169-176.

Some thoughts on the interpretation of steady-state evoked potentials

Steady-state evoked potentials are popular due to their easy analysis in frequency space and the availability of methods for objective response detection. However, the interpretation of steady-state responses can be challenging due to their origin as a sequence of responses to single stimuli. In the present paper, issues of signal extinction and some characteristics of higher harmonics are illustrated based on simple model data for those readers who do not regularly hobnob with frequency-space representations of data. It is important to realize that the absence of a steady-state response does not prove the lack of neural activity. For the same underlying reasons, namely constructive and destructive superposition of individual responses, comparisons of amplitudes between experimental conditions are prone to inaccuracies. Thus, before inferring physiology from steady-state responses, one should consider an alternative explanation in terms of signal composition.

Output-Sensitive 3D Line Integral Convolution

We propose an output-sensitive visualization method for 3D line integral convolution (LIC) whose rendering speed is largely independent of the data set size and mostly governed by the complexity of the output on the image plane. Our approach of view-dependent visualization tightly links the LIC generation with the volume rendering of the LIC result in order to avoid the computation of unnecessary LIC points: early-ray termination and empty-space leaping techniques are used to skip the computation of the LIC integral in a lazy-evaluation approach; both ray casting and texture slicing can be used as volume-rendering techniques. The input noise is modeled in object space to allow for temporal coherence under object and camera motion. Different noise models are discussed, covering dense representations based on filtered white noise all the way to sparse representations similar to oriented LIC. Aliasing artifacts are avoided by frequency control over the 3D noise and by employing a 3D variant of MIPmapping. A range of illumination models is applied to the LIC streamlines: different codimension-2 lighting models and a novel gradient-based illumination model that relies on precomputed gradients and does not require any direct calculation of gradients after the LIC integral is evaluated. We discuss the issue of proper sampling of the LIC and volume-rendering integrals by employing a frequency-space analysis of the noise model and the precomputed gradients. Finally, we demonstrate that our visualization approach lends itself to a fast graphics processing unit (GPU) implementation that supports both steady and unsteady flow. Therefore, this 3D LIC method allows users to interactively explore 3D flow by means of high-quality, view-dependent, and adaptive LIC volume visualization. Applications to flow visualization in combination with feature extraction and focus-and-context visualization are described, a comparison to previous methods is provided, and a detailed performance analysis is included.

Comparison of Approximate Quantum Simulation Methods Applied to Normal Liquid Helium at 4 K

The Feynman-Kleinert linearized path integral molecular dynamics (FK-LPI), ring polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) methods are applied to the simulation of normal liquid helium. Comparisons of the simulation results at the T = 4 K and rho = 0.01873 A-3 state point are presented. The calculated quantum correlation functions for the three methods show significant differences, both in the short time and in the intermediate regions of the spectrum. Our simulation results are also compared to the recent results of other approximate quantum simulation methods. We find that FK-LPI qualitatively agrees with other approximate quantum simulation results while CMD and RPMD predict a qualitatively different impulsive rebound in the velocity autocorrelation function. Frequency space analysis reveals that RPMD exhibits a broad high-frequency tail similar to that from quantum mode coupling theory and numerical analytic continuation approaches, while FK-LPI provides a somewhat more rapid decay at high frequency than any of these three methods. CMD manifests a high-frequency component that is greatly reduced compared with the other methods.

Frequency space environment map rendering

We present a new method for real-time rendering of objects with complex isotropic BRDFs under distant natural illumination, as specified by an environment map. Our approach is based on spherical frequency space analysis and includes three main contributions. Firstly, we are able to theoretically analyze required sampling rates and resolutions, which have traditionally been determined in an ad-hoc manner. We also introduce a new compact representation, which we call a spherical harmonic reflection map (SHRM), for efficient representation and rendering. Finally, we show how to rapidly prefilter the environment map to compute the SHRM ---our frequency domain prefiltering algorithm is generally orders of magnitude faster than previous angular (spatial) domain approaches.

Ioffe-Regel crossover for plane-wave vibrational excitations in vitreous silica

The first Ioffe-Regel crossover for vibrational plane waves (when wavelength and mean free path are comparable) has been investigated theoretically for models of vitreous silica $(v\ensuremath{-}{\mathrm{SiO}}_{2})$ constructed by molecular dynamics. The crossover is found to be from a state of weak scattering to one of strong scattering, not vibrational localization. Three methods have been used to investigate the crossover: an analysis of the time evolution of a vibrational plane wave, a spectral-density analysis in frequency space, and an analysis of the final scattered state in momentum space. The first Ioffe-Regel crossover frequency is found by all three methods to be $\ensuremath{\sim}1$ THz for $v\ensuremath{-}{\mathrm{SiO}}_{2},$ for both longitudinal and transverse polarizations. A second Ioffe-Regel crossover occurs at $\ensuremath{\sim}6$ THz for $v\ensuremath{-}{\mathrm{SiO}}_{2},$ corresponding to the frequency at which the mean free path is minimal (comparable to the interatomic spacing), and the spectral-density width is maximal (comparable to the frequency range of the vibrational density of states).

Spatial frequency analysis of optical lithography resolution enhancement techniques

A consistent frequency-space analysis of the effects of optical lithography resolution enhancement techniques including optical proximity correction, off-axis illumination, phase-shift masks, and imaging interferometric lithography is presented. The improvements for each of these techniques are directly related to the enhanced frequency-space coverage afforded. Optical proximity correction extends the frequency coverage out to ∼1.2–1.3×NA/λ where NA is the optical system numerical aperture and λ the exposure wavelength enabling κ1’s of ∼0.45 in the context of the usual Rayleigh resolution equation CD=κ1λ/NA. There are many possible configurations for off-axis illumination. For a quadrupole oriented at 45° to the (x, y) pattern axes, the maximum spatial frequency is extended to 2NA/λ or κ1∼0.43. Adding pupil plane filters to ensure a uniform modulation transfer function and orienting the quadrupole along the pattern axes allows extension to frequencies of 2NA/λ or κ1∼0.3. Phase shifts at the mask plane emphasize the high frequency image components by increasing the importance of the quadratic imaging terms and allow frequencies to 2NA/λ and κ1’s out to ∼0.35. Imaging interferometric lithography further extends the frequency coverage out to either (1+NA)/λ or 3NA/λ depending on the details with corresponding κ1 s of ∼0.23–0.2.

A fourier interpretation of the Frei-Chen edge masks

The orthogonal set of 3 × 3 Frei-Chen edge detection makes was proposed based on a vector space approach. The way the masks were chosen was not fully explained. We introduce an interpretation of the Frei-Chen masks in terms of eight-dimensional Fourier transform coefficient vectors. The linear transformation between the nine-dimensional Frei-Chen space and the eight-dimensional Fourier transform space is derived. We also propose a modified set of eight orthogonal masks based on the frequency space analysis.

Spectral analysis of electromagnetic vibrations in DC machines through the finite element method

The authors describe the FLUXMECA software package for calculating the mechanical transfer function of electrical machines, either static or with moving parts, for applied currents of any waveform. The solution method is based on magnetic sampling in space and time and on mechanical analysis in frequency space. The magnetic field is computed by the classical finite-element method for static machines coupled with the boundary integral method for machines with moving parts in order to take movement into account. Mechanical computations are performed by the finite-element method. The calculation of excitation forces, which uses a surface distribution of the local force density on ferromagnetic materials, leads to a correct determination of the resulting mechanical response of the structure. Consequently, the determination of the Fourier spectrum is quite easy even if it requires a large volume of data to take into account the movement of the rotor and its shaft. >

Photo-Deep-Level Fourier Spectroscopy in Semi-Insulating Bulk Materials

A new technique called photo-deep-level Fourier spectroscopy (photo-DLFS) for evaluating deep levels in semi-in-sulating materials is proposed. It is presented with a frequency space analysis that makes it possible to analyze the deep-level parameters, without correction for the complicated temperature dependence in the current-transient equation, using numerical calculation of the Fourier coefficients taken from the Fourier transforms of the transient current values. Seven deep levels were detected in semi-insulating undoped LEC GaAs crystals using this method. Also, a comparison is made with the photo-DLTS method.

Fourier interpretation of multiphase averaging theory

There has been considerable interest over the last two decades in developing averaging methods to change the scales of motion in multiphase transport theory. More recently, these averaging methods have been related to instrumentation windows. In this article we relate the averaging theory to impulse-response filters. Moreover, we perform a Fourier analysis in frequency space to indicate how the filters should attenuate low- and high-frequency noise. A generalized averaging theory is presented in the space of tempered distributions. The theory is a natural generalization of classical averaging theory.

Deep Level Fourier Spectroscopy for Determination of Deep Level Parameters

A new technique called deep-lebel Fourier spectroscopy (DLFS), is proposed. This is an efficient and convenient method for evaluating deep livels in semiconductors. The technique is presented with a frequency space analysis for the case of exponential capacitance transients. Taking the Fourier transforms of the transient capacitance values, the deep level emission rate is determined in sequence from various numerical calculations of the Fourier coefficients. This method makes it possible to analyze the deep level accurately and automatically without judgements of the peaks in the spectra. Computer simulation and experiments using the method for a p-type Si Schottky diode are demonstrated. Finally, a comparison is made with the DLTS method.