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Electric power utilities must ensure a consistent and undisturbed supply of power, with the voltage levels adhering to specified ranges. Any deviation from these supply specifications can lead to malfunctions in equipment. Monitoring the quality of supplied power is crucial to minimize the impact of fluctuations in voltage. Variations in voltage or current from their ideal values are referred to as \"power quality (PQ) disturbances,\" highlighting the need for vigilant monitoring and management. Signal processing methods are widely used for power system applications which include understanding of voltage disturbance signals and used for retrieval of signal information from the signals Different signal processing methods are used for extracting information about a signal. The method of Fourier analysis involves application of Fourier transform giving frequency information. The method of Short-Time Fourier analysis involves application of Short-Time Fourier transform (STFT) giving time–frequency information. The method of continuous wavelet analysis involves application of Continuous Wavelet transform (CWT) giving signal information in terms of scale and time where frequency is inversely related to scale. The method of discrete wavelet analysis involves application of Discrete Wavelet transform (DWT) giving signal information in terms of approximations and details where approximations and details are low and high frequency representation of original signal. In this paper, an attempt is made to perceive power quality disturbances in MATLAB using Fourier, Short-Time Fourier, Continuous Wavelet and Discrete Wavelet Transforms. Proper understanding of the signals can be possible by transforming the signals into different domains. An emphasis on application of signal processing techniques can be laid for power quality studies. The paper compares the results of each transform using MATLAB-based visualizations. The discussion covers the advantages and disadvantages of each technique, providing valuable insights into the interpretation of power quality disturbances. As the paper delves into the complexities of each method, it takes the reader on a journey of signal processing complexities, culminating in a nuanced understanding of power quality disturbances and their representations across various domains. The outcomes of this research, elucidated through energy values, 3D plots, and comparative analyses, contribute to a comprehensive understanding of power quality disturbances. The findings not only traverse theoretical domains but also find practical utility in real-world scenarios.

Vibrational spectroscopy techniques, such as Fourier-transform infrared (FTIR) and Raman spectroscopy, have been successful methods for studying the interaction of light with biological materials and facilitating novel cell biology analysis. Spectrochemical analysis is very attractive in disease screening and diagnosis, microbiological studies and forensic and environmental investigations because of its low cost, minimal sample preparation, non-destructive nature and substantially accurate results. However, there is now an urgent need for multivariate classification protocols allowing one to analyze biologically derived spectrochemical data to obtain accurate and reliable results. Multivariate classification comprises discriminant analysis and class-modeling techniques where multiple spectral variables are analyzed in conjunction to distinguish and assign unknown samples to pre-defined groups. The requirement for such protocols is demonstrated by the fact that applications of deep-learning algorithms of complex datasets are being increasingly recognized as critical for extracting important information and visualizing it in a readily interpretable form. Hereby, we have provided a tutorial for multivariate classification analysis of vibrational spectroscopy data (FTIR, Raman and near-IR) highlighting a series of critical steps, such as preprocessing, data selection, feature extraction, classification and model validation. This is an essential aspect toward the construction of a practical spectrochemical analysis model for biological analysis in real-world applications, where fast, accurate and reliable classification models are fundamental. A tutorial for multivariate classification analysis of vibrational spectroscopy data (Fourier-transform infrared, Raman and near-IR) is presented. Guidelines are provided for data preprocessing, data selection, feature extraction, classification and model validation.

Advances in sample preparation and computation analysis make FTIR of biological materials a rapidly expanding research area. Researchers from a number of universities have collaborated to provide procedures for FTIR analysis of biological samples. IR spectroscopy is an excellent method for biological analyses. It enables the nonperturbative, label-free extraction of biochemical information and images toward diagnosis and the assessment of cell functionality. Although not strictly microscopy in the conventional sense, it allows the construction of images of tissue or cell architecture by the passing of spectral data through a variety of computational algorithms. Because such images are constructed from fingerprint spectra, the notion is that they can be an objective reflection of the underlying health status of the analyzed sample. One of the major difficulties in the field has been determining a consensus on spectral pre-processing and data analysis. This manuscript brings together as coauthors some of the leaders in this field to allow the standardization of methods and procedures for adapting a multistage approach to a methodology that can be applied to a variety of cell biological questions or used within a clinical setting for disease screening or diagnosis. We describe a protocol for collecting IR spectra and images from biological samples (e.g., fixed cytology and tissue sections, live cells or biofluids) that assesses the instrumental options available, appropriate sample preparation, different sampling modes as well as important advances in spectral data acquisition. After acquisition, data processing consists of a sequence of steps including quality control, spectral pre-processing, feature extraction and classification of the supervised or unsupervised type. A typical experiment can be completed and analyzed within hours. Example results are presented on the use of IR spectra combined with multivariate data processing.

This protocol describes how in-solution protein FTIR can be used to obtain information about the relative contributions of α-helices, β-sheets, β-turn, and random coil structures to a protein's secondary structure. Fourier transform IR (FTIR) spectroscopy is a nondestructive technique for structural characterization of proteins and polypeptides. The IR spectral data of polymers are usually interpreted in terms of the vibrations of a structural repeat. The repeat units in proteins give rise to nine characteristic IR absorption bands (amides A, B and I–VII). Amide I bands (1,700–1,600 cm −1 ) are the most prominent and sensitive vibrational bands of the protein backbone, and they relate to protein secondary structural components. In this protocol, we have detailed the principles that underlie the determination of protein secondary structure by FTIR spectroscopy, as well as the basic steps involved in protein sample preparation, instrument operation, FTIR spectra collection and spectra analysis in order to estimate protein secondary-structural components in aqueous (both H 2 O and deuterium oxide (D 2 O)) solution using algorithms, such as second-derivative, deconvolution and curve fitting. Small amounts of high-purity (>95%) proteins at high concentrations (>3 mg ml −1 ) are needed in this protocol; typically, the procedure can be completed in 1–2 d.

In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: The key tools behind our results are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier transforms for functions such that their Fourier transforms are of monotone type or lacunary series.

A procedure for determining concentrations of lignin, cellulose, and hemicellulose in plant materials using Fourier-transform IR spectroscopy in the middle spectral region was developed and tested. The procedure is based on the use of calibration functions reflecting the dependence of the intensity of analytical absorption bands on the concentration of lignin (1512 cm –1 ) and cellulose (1450 cm –1 ) in model samples; for hemicellulose, indirect correlations were used. The model samples were ternary mixtures consisting of lignin, bacterial cellulose, and hemicellulose in various proportions. The proposed method was tested on a wide range of plant biomass samples; it demonstrated adequate precision (RSD no more than 4%). The accuracy of the procedure for determining the main components of plant biomass (lignin, cellulose, and hemicellulose) was demonstrated using the standard addition method.

New and creative methodologies for the fabrication of silver nanoparticles (Ag-NPs), which are exploited in a wide range of consumer items, are of significant interest. Hence, this research emphasizes the biological approach of Ag-NPs through Egyptian henna leaves ( Lawsonia inermis Linn.) extracts and analysis of the prepared Ag-NPs. Plant extract components were identified by gas chromatography mass spectrometry (GC-mass). The analyses of prepared Ag-NPs were carried out through UV–visible (UV–Vis), X-ray diffraction (XRD), transmission electron microscope (TEM), scanning electron microscope (SEM), and Fourier transform infrared (FTIR) analysis. UV–Vis reveals that Ag-NPs have a maximum peak at 460 nm in visible light. Structural characterization recorded peaks that corresponded to Bragg’s diffractions for silver nano-crystal, with average crystallite sizes varying from 28 to 60 nm. Antibacterial activities of Ag-NPs were examined, and it is observed that all microorganisms are very sensitive to biologically synthesized Ag-NPs.

Fourier transform infrared (FTIR) spectroscopy was introduced in 1991 as a technique to identify and classify microbes. Since then, it has gained growing interest and has undergone a remarkable evolution. Highly sophisticated spectrometers have been developed, enabling a high sample throughput. Today, the generation of high-quality data in a short time and the application of the technique for rapid and reliable identification of microbes to the species level are well documented. What makes FTIR spectroscopy even more attractive is the fact that spectral information can also be exploited for strain typing purposes, which is particularly important for epidemiological analyses and some technological applications. Accordingly, in recent years, FTIR spectroscopy has been increasingly used for typing and classifying microorganisms below the species level. The intention of this review is to give an overview over current knowledge and strategies of using FTIR spectroscopy for species identification and to describe different approaches for strain typing.

Rising global concentrations of environmental microplastics and nanoplastics (MNPs) drive concerns for human exposure and health outcomes. Complementary methods for the robust detection of tissue MNPs, including pyrolysis gas chromatography–mass spectrometry, attenuated total reflectance–Fourier transform infrared spectroscopy and electron microscopy with energy-dispersive spectroscopy, confirm the presence of MNPs in human kidney, liver and brain. MNPs in these organs primarily consist of polyethylene, with lesser but significant concentrations of other polymers. Brain tissues harbor higher proportions of polyethylene compared to the composition of the plastics in liver or kidney, and electron microscopy verified the nature of the isolated brain MNPs, which present largely as nanoscale shard-like fragments. Plastic concentrations in these decedent tissues were not influenced by age, sex, race/ethnicity or cause of death; the time of death (2016 versus 2024) was a significant factor, with increasing MNP concentrations over time in both liver and brain samples ( P  = 0.01). Finally, even greater accumulation of MNPs was observed in a cohort of decedent brains with documented dementia diagnosis, with notable deposition in cerebrovascular walls and immune cells. These results highlight a critical need to better understand the routes of exposure, uptake and clearance pathways and potential health consequences of plastics in human tissues, particularly in the brain. Pyrolysis gas chromatography–mass spectrometry reveals the presence of microplastics and nanoplastics in human kidney, liver and brain tissue samples from 2016 and 2024, with higher proportions found in the brain.

The fractional Fourier transform is critical in signal processing and supports many applications. Signal processing is one notable application. Implementing the fractional Fourier transform requires discrete versions. As a result, defining a discrete coupled fractional Fourier transform (DCFrFT) is essential. This paper presents a discrete version of the continuous, two-dimensional coupled fractional Fourier transform, which is not a tensor product of one-dimensional transforms. We examine the main characteristics of the operator and illustrate its relationship with the existing two-dimensional discrete fractional Fourier transforms. Examples help clarify the approach.