Fourier-based Analysis Research Articles

Nanometric determination of the thickness of aqueous samples for accurate molar absorption coefficients of water-soluble molecules in the mid-infrared region

Absorption spectra of aqueous samples measured by transmission need to be acquired using very thin cells (5–50 μm) when targeting the mid-infrared (mid-IR) region due to the strong background absorbance of liquid water. The thickness of the cell used controls the pathlength of the light through the sample, a value needed to transform absorption spectra into molar absorption coefficient spectra, or to determine solute concentrations from absorption spectra. The most accurate way to determine the thickness of an empty cell (i.e., filled with air) is from the period of an interference pattern, known as interference fringes, that arises when the cell is placed perpendicular to the path of light in the spectrometer. However, this same approach is not directly applicable to determine the thickness of a cell filled with an aqueous solution, due partially to the smaller amplitude of the interference fringes but fundamentally caused by its complex waveform, with a wavenumber-dependent oscillation period. Here, using Fresnel equations, we derived analytical expressions to model interference fringes in absorption spectra obtained by transmission, which are also valid for aqueous samples. We also present a novel Fourier-based analysis of the interference fringes that, in combination with the derived analytical expressions, allowed us to determine the pathlength of aqueous samples with an error below ∼ 50 nm. We implemented this novel approach to analyze interference fringes as a Live Script running in the software Matlab. As an application, we measured the absorption spectra of a 97 mM solution of MES buffer at pH 3.4 and pH 8.4 using cells of various nominal thicknesses (6, 25 and 50 μm), whose actual thicknesses were determined using the present approach. The derived molar absorption coefficient spectrum for both the acidic and basic forms of MES were virtually identical regardless of the cell, indicating that the determined thicknesses were likely very accurate. These results illustrate the utility of the present methodology in obtaining accurate molar absorption coefficient spectra of water-soluble molecules in the mid-IR region.

Comprehensive Multimode Reflection Analysis of a Dielectric-Loaded Rectangular Waveguide Terminated by Semi-Infinite Dielectric Media

This article presents a comprehensive multimode reflection analysis of a dielectric-loaded rectangular waveguide terminated by semiinfinite dielectric media. A Fourier-based analysis approach is extended for different incident modes of the waveguide to calculate the amplitude coefficients of the reflected modes when the flange or the waveguide walls have different finite conductivities. We calculate the complex propagation constant using the method of perturbation of the boundary conditions. The modal scattering parameters are defined based on the voltage wave normalized amplitudes to be valid for both propagating and evanescent fields. The inclusion of coupled and noncoupled modes in the solution is evaluated in terms of calculation time and the accuracy of the results. An algorithm is presented to calculate the reflection coefficient of variations in terms of the coupled modes included in the solution. It is shown that these variations are dependent on the operating frequency and dielectric properties used in the geometry. Our results are compared with 3-D full-wave simulations, and an excellent agreement is achieved over a wide frequency range by using the primary coupled modes in the solution. The modal aperture admittance is calculated for different modes to show the coupled modes’ effect on the results. Also, the proposed algorithm is modified to find the effective coupled modes much faster. These modes are used to obtain accurate results for different dielectric-loaded structures.

The impacts of the refugee population, renewable energy consumption, carbon emissions, and economic growth on health expenditure in Turkey: new evidence from Fourier-based analyses.

Health expenditures are affected by different macroeconomic variables. This study aims to examine the impact of renewable energy consumption, carbon emissions, the refugee population, and economic growth on Turkey's health expenditures from 1975 to 2019. For this purpose, firstly, the stationarity orders of the variables were examined with the Fourier-based stationarity test. The long-run effects of the variables on health expenditures were also examined using the Fourier-based cointegration test. The results show that there is a long-run relationship between health expenditures and the explanatory variables. In addition, long-run coefficients were calculated, and it was concluded that carbon emissions and the refugee population increased health expenditures while renewable energy consumption decreased. The causality results indicate that there is unidirectional permanent causality from health expenditures to renewable energy consumption and economic growth and bidirectional permanent causality between carbon emissions and health expenditures. Overall, adopting environmentally and renewable energy-friendly policies and controlling the refugee population are essential policy tools in terms of health expenditures.

Measuring the average cell size and width of its distribution in cellular tissues using Fourier transform.

We present an in-depth investigation of a fully automated Fourier-based analysis to determine the cell size and the width of its distribution in 3D biological tissues. The results are thoroughly tested using generated images, and we offer valuable criteria for image acquisition settings to optimize accuracy. We demonstrate that the most important parameter is the number of cells in the field of view, and we show that accurate measurements can already be made on volume only containing [Formula: see text] cells. The resolution in z is also not so important, and a reduced number of in-depth images, of order of one per cell, already provides a measure of the mean cell size with less than 5% error. The technique thus appears to be a very promising tool for very fast live local volume cell measurement in 3D tissues in vivo while strongly limiting photobleaching and phototoxicity issues.

Multiple metals influence distinct properties of the Arabidopsis circadian clock.

Circadian rhythms coordinate endogenous events with external signals, and are essential to biological function. When environmental contaminants affect these rhythms, the organism may experience fitness consequences such as reduced growth or increased susceptibility to pathogens. In their natural environment plants may be exposed to a wide range of industrial and agricultural soil pollutants. Here, we investigate how the addition of various metal salts to the root-interaction environment can impact rhythms, measured via the promoter:luciferase system. The consequences of these environmental changes were found to be varied and complex. Therefore, in addition to traditional Fourier-based analyses, we additionally apply novel wavelet-based spectral hypothesis testing and clustering methodologies to organize and understand the data. We are able to classify broad sets of responses to these metal salts, including those that increase, and those that decrease, the period, or which induce a lack of precision or disrupt any meaningful periodicity. Our methods are general, and may be applied to discover common responses and hidden structures within a wide range of biological time series data.

A Waveform-Independent Measure of Recurrent Neural Activity.

Rhythmic neural activity, so-called oscillations, plays a key role in neural information transmission, processing, and storage. Neural oscillations in distinct frequency bands are central to physiological brain function, and alterations thereof have been associated with several neurological and psychiatric disorders. The most common methods to analyze neural oscillations, e.g., short-time Fourier transform or wavelet analysis, assume that measured neural activity is composed of a series of symmetric prototypical waveforms, e.g., sinusoids. However, usually, the models generating the signal, including waveform shapes of experimentally measured neural activity are unknown. Decomposing asymmetric waveforms of nonlinear origin using these classic methods may result in spurious harmonics visible in the estimated frequency spectra. Here, we introduce a new method for capturing rhythmic brain activity based on recurrences of similar states in phase-space. This method allows for a time-resolved estimation of amplitude fluctuations of recurrent activity irrespective of or specific to waveform shapes. The algorithm is derived from the well-established field of recurrence analysis, which, in comparison to Fourier-based analysis, is still very uncommon in neuroscience. In this paper, we show its advantages and limitations in comparison to short-time Fourier transform and wavelet convolution using periodic signals of different waveform shapes. Furthermore, we demonstrate its application using experimental data, i.e., intracranial and noninvasive electrophysiological recordings from the human motor cortex of one epilepsy patient and one healthy adult, respectively.

Time-frequency analysis methods and their application in developmental EEG data

EEG provides a rich measure of brain activity that can be characterized as neuronal oscillations. However, most developmental EEG work to date has focused on analyzing EEG data as Event-Related Potentials (ERPs) or power based on the Fourier transform. While these measures have been productive, they do not leverage all the information contained within the EEG signal. Namely, ERP analyses ignore non-phase-locked signals and Fourier-based power analyses ignore temporal information. Time-frequency analyses can better characterize the oscillations contained in the EEG data. By separating power and phase information across different frequencies, time-frequency measures provide a closer interpretation of the neurophysiological mechanisms, facilitate translation across neurophysiology disciplines, and capture processes not observed by ERP or Fourier-based analyses (e.g., connectivity). Despite their unique contributions, a literature review of this journal reveals that time-frequency analyses of EEG are yet to be embraced by the developmental cognitive neuroscience field. This manuscript presents a conceptual introduction to time-frequency analyses for developmental researchers. To facilitate the use of time-frequency analyses, we include a tutorial of accessible scripts, based on Cohen (2014), to calculate time-frequency power (signal strength), inter-trial phase synchrony (signal consistency), and two types of phase-based connectivity (inter-channel phase synchrony and weighted phase lag index).

Characteristics of the wall temperature field in a mixed convection turbulent boundary layer

The behavior of the heated wall temperature field adjacent to a mixed convection turbulent boundary layer flow was investigated. The wall temperature field was captured using an infrared camera. The Richardson number was varied between experiments to produce a range of mixed convection conditions ranging from buoyancy dominant (RiL = 2.0) to inertia dominant (RiL = 0.01). From the 2D temperature fields recorded, the fluctuating temperature fields and associated low-order statistics were computed. A Fourier-based analysis of the fluctuating temperature field indicated the presence of multiple modes of energy exchange between heated wall and the adjacent turbulent boundary layer flow including energy input, dissipation, and a viscous-convective subrange for RiL ≤ 0.3. The Proper Orthogonal Decomposition (POD) was performed on the fluctuating temperature field. Results show cell-like patterns in low-order POD modes at all tested RiL suggesting a convective cell-like structure in the fluid region adjacent to the interface. The manifestation of these cell-like patterns was found to occur at increasing POD mode number as buoyant contributions decreased relative to inertial contributions.

A Study on Halftoning Improvement for Low-Resolution Digital Print Engines With Machine Learning Methods

As today’s printing volume worldwide decreases, and most traditional printing engines are expensive non-digital devices (offset), the demand for a low-cost digital replacement is rapidly increasing. A main disadvantage of digital presses is the low-resolution capabilities, introducing a compromise in the print quality (PQ). A key factor of print quality is the halftoning algorithm. A very common halftoning method is amplitude modulation (AM) halftone screening, in which dots are placed on a repetitive lattice, varying in size as a function of the grey level. The main AM screen design PQ challenge for low-resolution devices is the quantization frequencies, a disturbing pattern that usually emerges when a screen is approximated to a rational angle due to low resolution. Fourier-based analysis is a classical rule-based method to filter out screens that suffer from visually disturbing quantization patterns. This work presents a new approach that tackles this challenge by incorporating machine learning with the classic Fourier-based approach. Particularly, we show that a binary decision tree classifier with a Fourier-based feature vector has an accuracy of 95% in identifying quantization-free screens compared to the classic rule-based method, which has an accuracy of 66%. We conclude by demonstrating the use of the screen classifier to design a quantization-free screen set. This is done by first applying the screen classifier to the entire screen pool, that is, the set of all possible screens for a given print engine, followed by a rosette zero-moiré offset-like screen design.

Polarized light guiding anisotropic deformation and relaxation in photosensitive polymeric substrates

Light-responsive polymers offer unique possibilities for anisotropic manipulation of objects on the micron scale. Here we demonstrate the reversible anisotropic stretching of a polymeric surface made out of an azopolymer-elastomer blend, in response to green laser irradiation with varying polarization. We quantify the stretching parameters and the residual strain after relaxation by means of a Fourier-based analysis, which exploits a periodic 2D pattern imprinted onto the surface.

Revealing the Dynamic Nature of Amplitude Modulated Neural Entrainment With Holo-Hilbert Spectral Analysis.

Patterns in external sensory stimuli can rapidly entrain neuronally generated oscillations observed in electrophysiological data. Here, we manipulated the temporal dynamics of visual stimuli with cross-frequency coupling (CFC) characteristics to generate steady-state visual evoked potentials (SSVEPs). Although CFC plays a pivotal role in neural communication, some cases reporting CFC may be false positives due to non-sinusoidal oscillations that can generate artificially inflated coupling values. Additionally, temporal characteristics of dynamic and non-linear neural oscillations cannot be fully derived with conventional Fourier-based analyses mainly due to trade off of temporal resolution for frequency precision. In an attempt to resolve these limitations of linear analytical methods, Holo-Hilbert Spectral Analysis (HHSA) was investigated as a potential approach for examination of non-linear and non-stationary CFC dynamics in this study. Results from both simulation and SSVEPs demonstrated that temporal dynamic and non-linear CFC features can be revealed with HHSA. Specifically, the results of simulation showed that the HHSA is less affected by the non-sinusoidal oscillation and showed possible cross frequency interactions embedded in the simulation without any a priori assumptions. In the SSVEPs, we found that the time-varying cross-frequency interaction and the bidirectional coupling between delta and alpha/beta bands can be observed using HHSA, confirming dynamic physiological signatures of neural entrainment related to cross-frequency coupling. These findings not only validate the efficacy of the HHSA in revealing the natural characteristics of signals, but also shed new light on further applications in analysis of brain electrophysiological data with the aim of understanding the functional roles of neuronal oscillation in various cognitive functions.

A Novel Approach for the Characterization of Triangular Modulated Frequency Modulated Continuous Wave Low Probability of Intercept Radar Signals via Application of the Wigner-Ville Distribution

Digital intercept receivers are changing from Fourier-based analysis to classical time-frequency analysis techniques for analyzing low probability of intercept radar signals. This paper presents a novel approach of characterizing low probability of intercept triangular modulated frequency modulated continuous wave radar signals through utilization and direct comparison of the signal processing techniques Wigner-Ville Distribution versus the Reassigned Smooth Pseudo Wigner-Ville Distribution. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, chirp rate, and time-frequency localization (x and y direction). Also used were: percent detection, lowest signal-to-noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall, the Reassigned Smooth Pseudo Wigner-Ville Distribution signal processing technique produced more accurate characterization metrics than the Wigner-Ville Distribution signal processing technique.

Viscoelastic parameter estimation using simulated shear wave motion and convolutional neural networks

Ultrasound shear wave elastography (SWE) techniques have been very useful for the analysis of tissue rheological properties, but there are still obstacles for robust evaluation of viscoelastic tissue properties. In this proof-of-concept study, we investigate whether convolutional neural networks (CNN) are capable of retrieving the elasticity and viscosity parameters from simulated shear wave motion images. Staggered-grid finite difference simulations based on a Kelvin-Voigt rheological model were used to generate data for this study. The wave motion datasets were created using Kelvin-Voigt shear elasticity values ranging from 1 to 25 kPa, shear viscosities ranging from 0 to 10 Pa⋅s, and two different push profiles using f-numbers of 1 and 2. The CNN architectures, optimized using mean squared error loss, were then trained to retrieve a specific viscoelastic parameter. Both elasticity and viscosity values were successfully retrieved, with regression R2 values above 0.99 when correlating the estimated mechanical properties versus the true mechanical properties. The CNN performance was also compared to estimation of shear elasticity and viscosity from fitting dispersion curves estimated from two-dimensional Fourier transform analysis. The results demonstrated that the CNN models were robust to noise, vertical position and partially to f-number. The architecture was proven to be robust to multiple push profiles if trained properly. The CNN results showed higher accuracy over the full viscoelastic parameter range compared to the Fourier-based analysis. The overall results showed the CNNs’ potential to be an alternative to complex mathematical analyses such as Fourier analysis and dispersion curve estimation used currently for shear wave viscoelastic parameter estimation.

Detection and Parameter Extraction of Low Probability of Intercept Frequency Hopping Signals using the Spectrogram and the Reassigned Spectrogram

Low probability of intercept radar signals, which are often problematic to detect and characterize, have as their goal ‘to see and not be seen’. Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques for the purpose of analyzing these low probability of intercept radar signals. Although these classical time-frequency analysis techniques are an improvement over existing Fourier-based techniques, they still suffer from a lack of readability –which can be caused by poor time-frequency localization (such as the spectrogram), which may in turn lead to inaccurate detection and parameter extraction. In this study, the reassignment method, because of its ability to improve time-frequency localization, is proposed as an improved signal analysis technique to address the poor time-frequency localization deficiency of the spectrogram. This paper presents the novel approach of characterizing low probability of intercept frequency hopping radar signals through utilization and direct comparison of the spectrogram versus the reassigned spectrogram.

RIDF: A ROBUST ROTATION-INVARIANT DESCRIPTOR FOR 3D POINT CLOUD REGISTRATION IN THE FREQUENCY DOMAIN

Abstract. Registration of point clouds is a fundamental problem in the community of photogrammetry and 3D computer vision. Generally, point cloud registration consists of two steps: the search of correspondences and the estimation of transformation parameters. However, to find correspondences from point clouds, generating robust and discriminative features is of necessity. In this paper, we address the problem of extracting robust rotation-invariant features for fast coarse registration of point clouds under the assumption that the pairwise point clouds are transformed with rigid transformation. With a Fourier-based descriptor, point clouds represented by volumetric images can be mapped from the image to feature space. It is achieved by considering a gradient histogram as a continuous angular signal which can be well represented by the spherical harmonics. The rotation-invariance is established based on the Fourier-based analysis, in which high-frequency signals can be filtered out. This makes the extracted features robust to noises and outliers. Then, with the extracted features, pairwise correspondence can be found by the fast search. Finally, the transformation parameters can be estimated by fitting the rigid transformation model using the corresponding points and RANSAC algorithm. Experiments are conducted to prove the effectiveness of our proposed method in the task of point cloud registration. Regarding the experimental results of the point cloud registration using two TLS benchmark point cloud datasets, featuring with limited overlaps and uneven point densities and covering different urban scenes, our proposed method can achieve a fast coarse registration with rotation errors of less than 1 degree and translation errors of less than 1m.

Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation

A delayed detached eddy simulation of an overexpanded nozzle flow with shock-induced separation is carried out at a Reynolds number of , based on nozzle throat diameter and stagnation chamber properties. In this flow, self-sustained shock oscillations induce local unsteady loads on the nozzle wall as well as global off-axis forces. Despite several studies in the last few decades, a clear physical understanding of the factors driving this unsteadiness is still lacking. The geometry under investigation is a subscale truncated ideal contour nozzle, which was experimentally tested at the University of Texas at Austin at a nozzle pressure ratio of 30. Under these conditions, the nozzle operates in a highly overexpanded state and comprises a conical separation shock that merges to form a Mach disk at the nozzle centre. The delayed detached eddy simulation model agrees well with the experimental results in terms of mean and fluctuating wall-pressure statistics. Wall-pressure spectra reveal a large bump at low frequencies associated with an axisymmetric (piston-like) motion of the shock system, followed by a broad and high-amplitude peak at higher frequencies associated with the Mach waves produced by turbulent eddies convecting through the detached shear layer. Moreover, a distinct peak at an intermediate frequency ( ) persists in the wall-pressure spectra downstream of the separation shock. A Fourier-based analysis performed in both time and space (azimuthal wavenumber) reveals that this intermediate-frequency peak is associated with the (non-symmetric) pressure mode and is thus related to the generation of aerodynamic side loads. It is then shown how the unsteady Mach disk motion is characterized by an intense vortex shedding activity that, together with the vortical structures of the annular shear layer, contributes to the sustainment of an aeroacoustic feedback loop occurring within the nozzle.

Apparent stiffness of vimentin intermediate filaments in living cells and its relation with other cytoskeletal polymers

The cytoskeleton is a complex network of interconnected biopolymers intimately involved in the generation and transmission of forces. Several mechanical properties of microtubules and actin filaments have been extensively explored in cells. In contrast, intermediate filaments (IFs) received comparatively less attention despite their central role in defining cell shape, motility and adhesion during physiological processes as well as in tumor progression. Here, we explored relevant biophysical properties of vimentin IFs in living cells combining confocal microscopy and a filament tracking routine that allows localizing filaments with ~20 nm precision. A Fourier-based analysis showed that IFs curvatures followed a thermal-like behavior characterized by an apparent persistence length (lp*) similar to that measured in aqueous solution. Additionally, we determined that certain perturbations of the cytoskeleton affect lp* and the lateral mobility of IFs as assessed in cells in which either the microtubule dynamic instability was reduced or actin filaments were partially depolymerized. Our results provide relevant clues on how vimentin IFs mechanically couple with microtubules and actin filaments in cells and support a role of this network in the response to mechanical stress.

Low Probability of Intercept Triangular Modulated Frequency Modulated Continuous Wave Signal Characterization Comparison Using the Wigner Ville Distribution and the Choi Williams Distribution

Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time frequency analysis techniques for the purpose of analyzing low probability of intercept radar signals. This paper presents the novel approach of characterizing low probability of intercept triangular modulated frequency modulated continuous wave radar signals through utilization and direct comparison of the Wigner Ville Distribution versus the Choi Williams Distribution. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, chirp rate, and time-frequency localization (x and y direction). Also used were: percent detection, lowest signal-to noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall, the Wigner Ville Distribution produced more accurate characterization metrics than the Choi Williams Distribution. An improvement in performance may well translate into an increase in personnel safety.

A Data-Driven Multi-scale Technique for fMRI Mapping of the Human Somatosensory Cortex.

A previously introduced Bayesian non-parametric multi-scale technique, called iterated Multigrid Priors (iMGP) method, is used to map the topographic organization of human primary somatosensory cortex (S1). We analyze high spatial resolution fMRI data acquired at ultra-high field (UHF, 7T) in individual subjects during vibrotactile stimulation applied to each distal phalange of the left hand digits using both a travelling-wave (TW) and event-related (ER) paradigm design. We compare the somatotopic digit representations generated in S1 using the iMGP method with those obtained using established fMRI paradigms and analysis techniques: Fourier-based analysis of travelling-wave data and General Linear Model (GLM) analysis of event-related data. Maps derived with the iMGP method are similar to those derived with the standard analysis, but in contrast to the Fourier-based analysis, the iMGP method reveals overlap of activity from adjacent digit representations in S1. These findings validate the use of the iMGP method as an alternative to study digit representations in S1, particularly with the TW design as an attractive means to study cortical reorganization in patient populations such dystonia and carpal tunnel syndrome, where the degree of spatial overlap of cortical finger representations is of interest.

High-speed polarization-resolved third-harmonic microscopy

Polarization-resolved third-harmonic generation (P-THG) is a sensitive probe of material anisotropy and molecular ordering. Despite its promises, this property has little been used in biological tissues due to the lack of measurement schemes compatible with dynamic samples. We report here on the development of a fast P-THG microscope where excitation polarization is switched between line scans using an electro-optic modulator, providing temporal resolution in the 10 ms range for the polarimetric measurement. We demonstrate novel applications enabled by this approach, associated with Fourier-based analysis: probing molecular order in deforming lipid structures undergoing phase transition; revealing crystallinity of flowing particles in the zebrafish embryo’s inner ear; and detecting birefringence in vivo. These results establish that P-THG is ideally suited for probing lipid organization and mineralization in dynamic biological environments.