Spectral Averaging Research Articles

Rapid and non-invasive quantification of intramuscular fat content of intact pork cuts

Having acquired near infrared (NIR) hyperspectral images of intact pork loin samples through an NIR hyperspectral imaging system, the efficiency of a variety of image processing techniques including texture pattern analysis techniques were applied to process hyperspectral images so as to determine the intramuscular fat (IMF) content non-destructively. After the segmentation of region of interest (ROI), the raw spectral, texture-based spectral and textural characteristics of pork images were extracted by spectral averaging and pattern recognition techniques namely Gabor filter and improved gray level co-occurrence matrix (GLCM), respectively. First derivatives of the non-filtered and the Gabor filtered spectra were also investigated. Full waveband partial least squares regression (PLSR) was employed to determine the optimal parameters of Gabor filter and GLCM, and to select optimal wavelengths for IMF prediction. A stepwise procedure was applied to the optimal wavelengths to further optimize them to key wavelengths. Multiple linear regression (MLR) models were built based on the key wavelengths. Mean spectra and the Gabor filtered spectra outperformed GLCM. The best result, represented by correlation coefficients of calibration (Rc), cross validation (Rcv) and prediction (Rp) of 0.89, 0.89, and 0.86, respectively, was achieved using the first derivative of Gabor filtered spectra at 1193 and 1217 nm. To visualize the IMF content in pork, the distribution maps of IMF content in pork were drawn using a mean spectra-based MLR model. These promising results highlight the great potential of NIR hyperspectral imaging for non-destructive prediction of IMF content of intact pork.

Direct integrals and spectral averaging

A one parameter family of selfadjoint operators gives rise to a corresponding direct integral. We show how to use the Putnam-Kato theorem to obtain a new method for the proof of a spectral averaging result.

Comprehensive Analysis of LC/MS Data Using Pseudocolor Plots

We have developed new applications of the pseudocolor plot for the analysis of LC/MS data. These applications include spectral averaging, analysis of variance, differential comparison of spectra, and qualitative filtering by compound class. These applications have been motivated by the need to better understand LC/MS data generated from analysis of human biofluids. The examples presented use data generated to profile steroid hormones in urine extracts from a Cushing's disease patient relative to a healthy control, but are general to any discovery-based scanning mass spectrometry technique. In addition to new visualization techniques, we introduce a new metric of variance: the relative maximum difference from the mean. We also introduce the concept of substructure-dependent analysis of steroid hormones using precursor ion scans. These new analytical techniques provide an alternative approach to traditional untargeted metabolomics workflow. We present an approach to discovery using MS that essentially eliminates alignment or preprocessing of spectra. Moreover, we demonstrate the concept that untargeted metabolomics can be achieved using low mass resolution instrumentation.

ULTRA-HIGH-RESOLUTION INTENSITY STATISTICS OF A SCINTILLATING SOURCE

We derive the distribution of flux density of a compact source exhibiting strong diffractive scintillation. Our treatment accounts for arbitrary spectral averaging, spatially-extended source emission, and the possibility of intrinsic variability within the averaging time, as is typical for pulsars. We also derive the modulation index and present a technique for estimating the self-noise of the distribution, which can be used to identify amplitude variations on timescales shorter than the spectral accumulation time. Our results enable a for direct comparison with ultra-high resolution observations of pulsars, particularly single-pulse studies with Nyquist-limited resolution, and can be used to identify the spatial emission structure of individual pulses at a small fraction of the diffractive scale.

단일 비트 전자-광학 시그마-델타 변조기의 성능 및 지터 효과 분석

Electro-optical sigma-delta modulators are the core module of digital receiver to digitize wideband radio-frequency signals directly at an antenna. Electro-optical sigma-delta modulators use a pulsed laser to oversample an input radio-frequency signals at two Mach-Zehnder Interferometer(MZI) and shape the quantization noise using a fiber-lattice accumulator. Decimation filtering is applied to the quantizer output to construct the input signal with high resolution. The jitter affects greatly on reconstructing the original input signal of modulator. This paper analyzes the performance of first order single bit electro-optical sigma-delta modulator in the time domain and the frequency domain. The performance of modulator is analyzed by using asynchronous spectral averaging of the reconstructed signal`s spectrum in the frequency domain. The reference value of time jitter is presented by analyzing the performance of jitter effects. This kind of jitter value can be used as a reference value on the design of modulators.

Assessing the Influence of Fourier Analysis Parameters on Short-Time Modal Parameter Extraction

It is sometimes necessary to determine the manner in which materials and structures deteriorate with respect to time when subjected to sustained random dynamic loads. In such cases a system’s fatigue characteristics can be obtained by continuously monitoring its modal parameters. This allows for any structural deterioration, often manifested as a loss in stiffness, to be detected. Many common structural integrity assessment techniques make use of Fourier analysis for modal parameter extraction. For continual modal parameter extraction, the Fourier transform requires that a compromise be made between the accuracy of the estimates and how frequently they can be obtained. The limitations brought forth by this compromise can be significantly reduced by selecting suitable values for the analysis parameters, mainly subrecord length and number of averages. Further improvements may also be possible by making use of spectral enhancement techniques, specifically overlapped averaging and zero padding. This paper uses the statistical analysis of results obtained from numerous physical and numerical experiments to evaluate the influence of the analysis parameters and spectral enhancement techniques on modal estimates obtained from limited data sets. This evaluation will assist analysts in selecting the most suitable inputs for parameter extraction purposes. The results presented in this paper show that when using the Fourier transform to extract modal characteristics, any variation in the parameters used for analysis can have a significant influence on the extraction of natural frequency estimates from systems subjected to random excitation. It was found that for records containing up to 10% noise, subrecord length; hence spectral resolution, has a more pronounced influence on the accuracy of modal estimates than the level of spectral averaging; therefore spectral uncertainty. It was also found that while zero padding may not increase the actual spectral resolution, it does allow for improved natural frequency estimates with the introduction of interpolated estimates at the nondescribed frequencies. Finally, it was found that for modal parameter extraction purposes (in this case natural frequency), increased amounts of overlapped averaging can significantly reduce the variance of the estimates obtained. This is particularly useful as it allows for increased precision without compromising temporal resolution.

Geometric Methods for Spectral Analysis

This paper explores a geometric framework for modeling nonstationary but slowly varying time series, based on the assumption that short-windowed power spectra capture their spectral character, and that energy transference in the frequency domain has a physical significance. The framework relies on certain notions of transportation distance and their respective geodesics to model possible nonparametric changes in the power spectral density with respect to time. We discuss the relevance of this framework to applications in spectral tracking, spectral averaging, and speech morphing.

Enhancement of coherence functions using time signals in Modal Analysis

Experimental Modal Analysis (EMA) and Operational Modal Analysis (OMA) are two widely used techniques in the identification of modal parameters. EMA is synonymous with a laboratory environment requiring complete system shutdown while OMA is implemented in a real environment where the ambient forces cannot be isolated. A new method, namely Impact-Synchronous Modal Analysis (ISMA) utilising the modal extraction techniques commonly used in EMA but performed in the presence of the ambient forces, is proposed. Transfer functions, from where the modal parameters are extracted, are obtained from Fourier transform of cross and auto correlation functions. These functions are estimated quantities and their outcomes are dependable on the averaging techniques used. The coherence functions are commonly used to measure the acceptability of the estimations. Impact-Synchronous Time Averaging is compared against Spectral Averaging while performing Modal Analysis in a situation containing ambient and operating forces. Results showed that while the transfer functions obtained from both the averaging techniques were of similar quality, the Impact-Synchronous Time Averaging indicated better coherence than the Spectral Averaging.

Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix

We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a spectral averaging technique from the theory of random Schrödinger operators. The similar question for Hankel matrices remains open

Continuity of spectral averaging

We consider averages $\kappa$ of spectral measures of rank one perturbations with respect to a $\sigma$-finite measure $\nu$. It is examined how various degrees of continuity of $\nu$ with respect to $\alpha$-dimensional Hausdorff measures ($0 \leq \alpha \leq 1$) are inherited by $\kappa$. This extends Kotani’s trick where $\nu$ is simply the Lebesgue measure.

Some Applications of the Perturbation Determinant in Finite von Neumann Algebras

AbstractIn the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements H0 and H in the algebra and relate it to the concept of the de la Harpe-Skandalis homotopy invariant determinant associated with piecewise C1-paths of operators joining H0 and H. We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman-Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier-Fuglede-Kadison differentiation formula.

An Accurate-Mass-Based Spectral-Averaging Isotope-Pattern-Filtering Algorithm for Extraction of Drug Metabolites Possessing a Distinct Isotope Pattern from LC-MS Data

Detection and identification (ID) of all drug metabolites following liquid chromatography (LC)/mass spectrometry (MS) analysis of complex biological matrixes are not trivial. To facilitate detection of drug-derived materials that possess highly diagnostic isotopic patterns (e.g., chlorine- and bromine-containing compounds), we report an accurate-mass-based spectral-averaging isotope-pattern-filtering (AMSA-IPF) algorithm developed in the computational language R. The AMSA-IPF algorithm offers three significant improvements over the traditional isotope filtering method often provided by instrument vendors. First, spectral averaging is performed before the IPF to reduce scan-to-scan variability of ion intensities. Second, the IPF process is strictly based on accurate mass typically obtained on high resolution mass spectrometers. The designated isotopic ion-pairs (e.g., M + 2:M or M + 1:M, where M is the molecular ion and M + 1 and M + 2 are the isotopic ions) must fall into the predefined accurate mass tolerance window (e.g., 5 ppm) and at the same time satisfy the predefined relative abundance criteria. Third, both M + 1:M and M + 2:M ion pairs are inspected in the filtering process. The inclusion of M + 1:M ion pair enhanced the specificity of this algorithm by removing background ions that form M:M + 2 ion pairs within predefined isotope ratios by coincidence. The algorithm demonstrated excellent effectiveness in detecting drug-related ions in in vivo samples (plasma, bile, urine and feces) obtained from rats orally dosed with 14C-loratadine. The ion chromatograms of the filtered LC-MS data files showed near perfect qualitative correlation with the corresponding radioprofiles. AMSA-IPF will be another great tool to facilitate detection and ID of drug metabolites in complex LC-MS data without the help of radiolabels. The AMSA-IPF algorithm is applicable to not only compounds containing distinct natural isotopes (such as Cl and Br) but also compounds that contain synthetically incorporated isotopes (13C, 15N, etc) generating a distinct isotope pattern. The ability to detect and identify metabolites from nonradiolabeled studies will be extremely beneficial to achieve compliance with FDA's most recent guidance on metabolites in safety testing (MIST).

Fat Distribution Analysis in Salmon Fillets Using Non-Contact near Infrared Interactance Imaging: A Sampling and Calibration Strategy

An online NIR interactance imaging instrument was tested for fat distribution analysis in raw and salted salmon fillets. Approximately 3000 spectra were collected for each fillet when passing under the instrument on a conveyor belt (approximately 1s exposure). The instrument was calibrated using five cylindrical plugs (15 mm diameter) from each fillet. The fat content was measured for each of these plugs using 1H-NMR spectrometry and the spectra from each plug region were averaged and used for calibration and validation. It was found that online NIR interactance imaging is well-suited for distributional fat analysis in raw and salted intact salmon fillets. The local sampling and calibration strategy using 15 mm diameter plugs for reference analysis and spectral averaging was found to provide relevant information and robust models. The average prediction errors (root mean square error of cross-validation) for raw and salted fillets in combination were approximately 2% fat for local plug regions.

Extending the Dynamic Range of a Spectrum Monitor Using Comparison Switching and Spectral Averaging

The dynamic range of a spectrum monitor can be extended by incoherently averaging the difference between the spectrum from the antenna and the spectrum from a comparison load. We show that it is often advantageous to increase the attenuation to the spectrum analyzer, thereby lowering the maximum signal strength at the mixer and subsequently compensating for the added noise by incoherent spectral averaging. We analyzed the case of a conventional heterodyne analyzer as well as an analyzer using direct analog-to-digital conversion (ADC) sampling.

Tachyonic γ -ray wideband of an ultra-relativistic electron plasma: Spectral fitting with Fermi power-law densities

Fermionic power-law distributions are derived by the second quantization of classical power-law ensembles, and applied to ultra-relativistic electron populations in the Galactic center. The γ -ray flux from the direction of the compact central source Sagittarius A* is fitted with a superluminal cascade spectrum. In this way, estimates of the radiating electron plasma in the Galactic center region are obtained, such as the power-law index, temperature, particle number, and internal energy. The spectral averaging of the tachyonic radiation densities with Fermi power-laws is explained. Fugacity expansions of the thermodynamic variables (thermal equation of state, entropy, isochoric heat capacity, and isothermal compressibility) are obtained in the quasiclassical high-temperature/low-density regime, where the spectral fit is carried out. The leading quantum correction to these variables is calculated, and its dependence on the electronic power-law index and the thermal wavelength is discussed. Excess counts of cosmic rays from the Galactic center region are related to the plasma temperature inferred from the cascade fit.

Speckle structure of a light field scattered by human eye retina

The speckle structure of a light field resulting from laser radiation scattering by human eye retina is analyzed. The presence of a speckle structure in the radiation scattered by an eye substantially impedes wave-front measurements in the study of aberrations. Two methods for suppressing such a structure based on the spatial and spectral averaging of the realizations of the speckle field are considered. The results of the theoretical calculation and numerical simulation are in agreement with the experimental data.

Thermodynamic variables of microquasars inferred from tachyonic spectral maps

Tachyonic spectral densities of ultra-relativistic electron populations are fitted to the γ-ray spectra of two microquasars, LS 5039 and LSI +61°303. The superluminal spectral maps are obtained from BATSE, COMPTEL, EGRET, HESS, and MAGIC data sets. The spectral averaging is done with exponentially cut power-law densities. Estimates of the electron distributions generating the tachyon flux are obtained from the spectral fits, such as power-law indices, electron temperature and source counts. The internal energy and heat capacities of the source populations are calculated. An extensive entropy functional is defined for Boltzmann power-law densities and its stability is checked. The high-temperature limit of the thermodynamic variables is determined by the power-law index of the electron plasma, which enters in the scaling exponents as well as the amplitudes.

Mesoscopic fluctuations of off-diagonal matrix elements of the angular momentum and orbital magnetism of free electrons in a rectangular box

We study, analytically and numerically, mesoscopic fluctuations of the off-diagonal matrix elements of the orbital angular momentum between the nearest energy levels $i=({n}_{x},{n}_{y})$ and $f=({k}_{x},{k}_{y})$ in a rectangular box with incommensurate sides. In the semiclassical regime, where the level number of $i$ is $\mathcal{N}⪢1$, our derivation gives $⟨{\ensuremath{\mid}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{if}\ensuremath{\mid}}^{2}⟩\ensuremath{\sim}\sqrt{\mathcal{N}}$. Numerical simulations, using simultaneous ensemble averaging (over the aspect ratios of rectangles) and spectral averaging (over the energy interval), are in excellent agreement with this analytical prediction. Physically, the mean is dominated by the level pairs ${k}_{x}={n}_{x}\ifmmode\pm\else\textpm\fi{}1$ and ${k}_{y}={n}_{y}\ensuremath{\mp}1$. Also in a rectangular box, we investigate the mean orbital susceptibility of a free-electron gas and argue that it reduces, up to a coefficient, to the two-level Van Vleck susceptibility that involves the last occupied (Fermi) level $i$ and the first unoccupied level $f$. This result is confirmed numerically as well, albeit the effect of fluctuations being more pronounced for the susceptibility since it is due to large fluctuations in both $⟨{\ensuremath{\mid}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{L}}_{if}\ensuremath{\mid}}^{2}⟩$ and in level separations ${\ensuremath{\epsilon}}_{f}\ensuremath{-}{\ensuremath{\epsilon}}_{i}$ (level bunching).

The k-moment method for modeling the blackbody weighted transmission function for narrow and wide band radiative properties of gases

This paper presents the k -moment method, based on the calculation of the moments of the absorption coefficient, to calculate the blackbody-weighted transmission function for modeling narrow and wide band radiative properties of gases. The spectral averaging is performed on band widths of the order from 25 to 600 cm - 1 . The spectrally averaged integral formulation of the radiative transfer equation is established and associated blackbody-weighted transmission function approximate expressions are derived from a series reversion technique. The second and third order k -moment formulations are assessed through comparisons with line-by-line reference results in the case of pure carbon dioxide at atmospheric pressure and for temperatures ranging from 300 up to 2300 K.

Distinguishing Individual Vibrational Fingerprints: Single-Molecule Surface-Enhanced Resonance Raman Scattering from One-to-One Binary Mixtures in Langmuir−Blodgett Monolayers

Here, it is demonstrated that similar chemical species within a multicomponent sample can be distinguished, down to the single-molecule level, by means of their surface-enhanced vibrational fingerprints. Surface-enhanced resonance Raman scattering spectra and 2D spatial intensity maps are recorded from thin Ag nanoparticle films coated with fatty acid Langmuir-Blodgett monolayers containing one-to-one binary mixtures, at varying concentrations, of two dye molecules of similar absorption and scattering cross section (n-pentyl-5-salicylimidoperylene and octadecylrhodamine B). The results reveal the change in the distribution of the two dyes within the monolayer, and the breakdown of ensemble spectral averaging, which occur as the single-molecule regime is approached. It is found that the unimolecular level is reached when 1-10 molecules of each dye occupy the 1-microm2 scattering areas probed by the laser. These signals are attributed to the rare spatial coincidence of isolated target analyte molecules and localized electromagnetic hot spots in the nanostructured metal film. The bianalyte nature of the samples provides strong corroborative support for the attribution of spectra to single molecules at high dilution, while the effect of domain formation/aggregation is found to be important at higher concentrations.