Basis Of Fourier Analysis Research Articles

Boosting unsupervised domain adaptation: A Fourier approach

By using unsupervised domain adaptation (UDA), knowledge is transferred from a label-rich source domain to a target domain that contains relevant information but has no labels. Most existing UDA algorithms primarily align domain-invariant features are primarily aligned during training, whereas target-specific information is ignored when learning the domain-invariant features. To address this issue, we attempted to boost the performance of unsupervised domain adaptation using a Fourier approach (FUDA). Specifically. FUDA is inspired by the fact that the amplitude of the Fourier spectrum mainly primarily preserves low-level statistics. Thus, the source domain can be augmented in FUDA to effectively equip with some low-level information in a target domain by fusing the amplitude of the two domains in the Fourier domain. Meanwhile, we propose Fourier transform channel attention, which represents the weight of Fourier transform to capture feature diversity. On the basis of Fourier analysis, we further show that the conventional attention that is built upon global average pooling is a special case of our proposed attention. Our method is evaluated by using four domain adaptation benchmarks, such as Office-31, Office-Home, VisDA-2017 and DomainNet, demonstrating the effectiveness of our FUDA.

Analysis and prediction of grain temperature from air temperature to ensure the safety of grain storage

ABSTRACT Food security is an influential factor for the development and future of humanity. Stored grain temperature is a key physical variable for grain quality control and management in stored-grain ecosystem. In this study, a prediction model using Fourier series based on least-squares method is introduced to describe the average temperature movement of grain pile and the daily air temperature, naming hysteresis cycle model (HCM). Then the HCM based on the Fourier analysis is proposed that incorporating with the least-squares method, the Fourier series model is applied to forecast the grain pile temperature from the daily air temperature. The HCM is built by finding relationship called conversion coefficients between the air and grain pile temperature that is constructed on the basis of Fourier analysis, and the optimal order of the model is determined by Akaike information criteria. Our method can reflect the time lag of the grain pile temperature changes with the change of air temperature and requires only a single variable (i.e. air temperature). Experiments including model fitting, temperature prediction, and results comparison for a period of 425 days from a real-world granary, yield satisfied results agreeing well with actual observation values. As a result of model validation, the proposed method has the root mean square error (RMSE) values ranging from 1.6°C to 2.3°C with average RMSE of 1.9°C. In other words, the proposed model can predict grain pile temperature with a high accuracy once an acceptable relationship between air temperature and grain pile temperature has been constructed from previously temperature data. Result analysis indicates effectiveness and workability of the proposed model for stored grain temperature prediction.

Обработка томографических изображений при помощи вейвлет-анализа

The paper is devoted to the problem of processing of tomographic images using wavelet analysis. The features of image processing techniques, indications were analyzed. Wavelets are a signal waveform of limited duration that has an average value of zero. Wavelets are comparable to a sine wave, and they are the basis of Fourier analysis. Wavelet analysis method allows to processing of tomographic images using a large time interval, where more accurate information about the low frequency region and shorter when information is needed on high frequency. The characteristic features of the settings wavelet transforms are described. Their bad choice reduces the reliability of detection of changes in the structure of signals when changing system state. The key stages of the reconstruction tomography images in DICOM format using the method of wavelet analysis were examined; algorithm of noise reduction was investigated. Practical area of application of wavelet analysis doesn´t limited to digital signal processing; it also covers physical experiments, numerical methods and other areas of physics and mathematics. By being able to analyze the non-stationary signals, wavelet analysis has become a powerful alternative Fourier transform in medical applications.

Recovery of Absolute Gas Absorption Line Shapes Using Tuneable Diode Laser Spectroscopy with Wavelength Modulation ¿ Part I: Theoretical Analysis

Tunable diode laser spectroscopy is extremely important for gas detection in a wide variety of industrial, safety and environmental monitoring applications. Of particular interest is the development of calibration-free, stand-alone systems and instrumentation which can operate in high-temperature or high-pressure environments (such as in fuel cells, or gas turbine engines) where continuous and simultaneous monitoring of pressure, temperature and concentration of gases may be required. Here, in Part 1 of this two-part paper, we present the full theoretical basis and range of techniques for calibration-free line-shape recovery to allow simultaneous measurements of concentration and pressure/temperature for a wide range of potential applications. Firstly, on the basis of Fourier analysis, we present the general signal components that arise with both intensity and frequency modulation of diode lasers and identify the issues and difficulties associated with accurate line-shape recovery in conventional wavelength modulation spectroscopy (WMS). We then show how line-shape recovery may be effectively performed using first harmonic signals and, by use of a general correction function from Fourier coefficients, we extend the techniques previously reported to include arbitrary large modulation indices, different line-shape profiles and high gas concentration with non-linear absorption. Previous approximate techniques based on Taylor series expansions are included as a special case of the Fourier analysis for low modulation indices. We also show that the signal amplitudes obtained in this way can be comparable to, or even exceed, that of conventional WMS by appropriate choice of the modulation index and frequency.

Q-type bursts in magnetic oscillations of ELF range as a phenomenon reflecting the properties of the global Earth-ionosphere resonator

The observation results of Q-type bursts in the measurements of the horizontal component of the noise magnetic field in the range of the first Schumann resonance in polar regions (Lovozero high-latitude observatory) are presented. Automatic selection of Q-type bursts from the experimental data series is implemented on the basis of a waveform recognition algorithm. The resonant nature of Q-bursts is shown. The possibility of selecting such events in magnetic excitation conditions is highlighted. The global resonator quality upon decreasing the selected waveform amplitudes is estimated. The data obtained by this method are compared with estimates on the basis of Fourier analysis and values known from the world literature. The possible reasons for disagreements of the estimates are analyzed, including the problem of selecting the function approximating the spectrum, the problem of accounting for the background, and the possible irregularity of the spectrum. It is shown that Q-type bursts, besides the quality, allow estimating the resonant frequency of the first oscillation mode; however, the accuracy of such estimation is lower as compared to the results of Fourier analysis methods.

Gene expression model (in)validation by Fourier analysis

BackgroundThe determination of the right model structure describing a gene regulation network and the identification of its parameters are major goals in systems biology. The task is often hampered by the lack of relevant experimental data with sufficiently low noise level, but the subset of genes whose concentration levels exhibit an oscillatory behavior in time can readily be analyzed on the basis of their Fourier spectrum, known to turn complex signals into few relatively noise-free parameters. Such genes therefore offer opportunities of understanding gene regulation quantitatively.ResultsFourier analysis is applied to data on gene expression levels in mouse liver cells that oscillate according to the circadian rhythm. Several model structures in the form of linear and nonlinear differential equations are matched to the data and it is shown that although the considered models can reproduce many features of the oscillatory patterns, some can be excluded on the basis of Fourier analysis without appeal to prior knowledge of regulatory pathways. A systematic method for testing models is also proposed based on measuring the effects of variations in gene copy-number on the expression levels of coupled genes.ConclusionsFourier analysis is a technique that is well-adapted to the study of biological oscillators and can be used instead or in addition to conventional modeling techniques. Its usefulness will increase as more high-resolution data become available.

Fourier analysis of HRTEM image deterioration caused by mechanical vibration.

Contrast deterioration of high-resolution transmission electron microscope (HRTEM) images, that is caused by mechanical vibrations of the turbo molecular pump (TMP), was systematically and quantitatively investigated on the basis of Fourier analysis using plural images. It was demonstrated that TEM image contrast was considerably deteriorated by the resonance of mechanical vibration at specific rotational speeds of the TMP. By setting a TMP rotational speed from 48,000 rotations per minute (rpm) to 41,000 rpm, apart from the mechanical resonance frequencies of the present apparatus, the information limit of the observed image was improved from 6 nm-1 to 7 nm(-1).

X-Ray Powder Diffraction Studies on the Rehydration Properties of Beidellite

AbstractThe rehydration properties of Ca-, Mg-, Na-, and K-saturated homoionic beidellites after heating at various temperatures were compared with those of montmorillonites. The behavior of interlayer Na+ during dehydration and rehydration was also investigated by means of one-dimensional Fourier analysis. The K- and Mg-saturated specimens exhibited fast and slow rehydration rates, respectively, during exposure to air of 50% RH after heating at 800°C. These homoionic specimens showed strong rehydration properties on saturation with deionized water after heating <900°C for 1 hr. On the basis of Fourier analysis, the interlayer cations appeared to have migrated into the hexagonal holes of SiO4 network on thermal dehydration, and the migrated cations returned to the interlayer space on rehydration. This behavior of the interlayer cations appears to have been strongly dependent on value of the octahedral negative charge and on the sizes of interlayer cations. The small octahedral negative charge of beidellite produced a weaker attractive electrostatic force between the octahedral sheets and the migrated interlayer cations. Therefore, the migrated interlayer cations in beidellite were easily extracted from the hexagonal holes, and rehydration was rapid. The small cation migrated easily into hexagonal holes and was fixed to the holes. On the contrary, large cations were probably difficult to fix and were easily extracted from the hexagonal holes. Consequently, the rehydration rate of K-saturated beidellite was fast, and that of Mg-saturated beidellite was slow.

Modulation Spaces on the Euclidean $n$-Space

The paper deals with the problem of the traces of functions belonging to modulation spaces on the basis of Fourier analysis and maximal inequalities.

Protonation-induced variability of electronic effects of silyl and germyl substituents in α-carbofunctional derivatives

On the basis of Fourier analysis of internal rotation curves for α-carbofunctional derivatives of Group IVb elements the effect of protonation of parent molecules on the nature of electronic effects of methyl, silyl and germyl substituents is discussed.