Savitzky-Golay Filter Research Articles

Digital image noise removal towards soybean and cotton plant disease using image processing filters

The processing of noisy images does not provide accurate outcomes. In most existing techniques, many filters have been employed to eradicate the noises and enhance the image quality. However, most of the works fail to generate enhanced outcomes because of degraded capability and increased time consumption. Hence, in the proposed research work, a novel pre-processing method called the optimization assisted cascaded filtering approach (OptCFA) is introduced. In the proposed Opt_CFA model, the Gaussian Amended Bilateral filter (GABF) is designed where the multilevel thresholds are calculated for the GABF outcomes. The filter parameters are optimized using the Amended Pelican optimization algorithm (AmPel) for first stage noise removal. The outcomes are then cascaded with an Extended Savitzky-Golay filter (E_SGF) for second stage noise removal. The proposed Opt_CFA model is a single approach with the integration of GABF, AmPel and E_SGF methods. In the results section, some existing pre-processing filters, like the median, bilateral, and Gaussian filters, are analyzed for comparison. The individual performance of GABF and E_SGF methods used in the proposed model are also analyzed. Through the proposed technique, the noises can be extensively removed, and the image quality can be greatly enhanced. Several existing filters are compared with the proposed model, whereas the results are analyzed using PYTHON.

An Investigation into the Application of Acceleration Responses' Trendline for Bridge Damage Detection Using Quadratic Regression.

It has been proven that structural damage can be successfully identified using trendlines of structural acceleration responses. In previous numerical and experimental studies, the Savitzky-Golay filter and moving average filter were adjusted to determine suitable trendlines and locate structural damage in a simply supported bridge. In this study, the quadratic regression technique was studied and employed to calculate the trendlines of the bridge acceleration responses. The normalized energies of the resulting trendlines were then used as a damage index to identify the location and severity of the structural bridge damage. An ABAQUS model of a 25 m simply supported bridge under a truckload with different velocities was used to verify the accuracy of the proposed method. The structural damage was numerically modeled as cracks at the bottom of the bridge, so the stiffness at the damage positions was decreased accordingly. Four different velocities from 1 m/s to 8 m/s were used. The proposed method can identify structural damage in noisy environments without monitoring the dynamic modal parameters. Moreover, the accuracy of the newly proposed trendline-based method was increased compared to the previous method. For velocities up to 4 m/s, the damage in all single- and multiple-damage scenarios was successfully identified. For the velocity of 8 m/s, the damage in some scenarios was not located accurately. Additionally, it should be noted that the proposed method can be categorized as an online, quick, and baseline-free structural damage-detection method.

Cascaded Thinning in Upscale and Downscale Representation for EEG Signal Processing.

Smoothing filters are widely used in EEG signal processing for noise removal while preserving signals' features. Inspired by our recent work on Upscale and Downscale Representation (UDR), this paper proposes a cascade arrangement of some effective image-processing techniques for signal filtering in the image domain. The UDR concept is to visualize EEG signals at an appropriate line width and convert it to a binary image. The smoothing process is then conducted by skeletonizing the signal object to a unit width and projecting it back to the time domain. Two successive UDRs could result in a better-smoothing performance, but their binary image conversion should be restricted. The process is computationally ineffective, especially at higher line width values. Cascaded Thinning UDR (CTUDR) is proposed, exploiting morphological operations to perform a two-stage upscale and downscale within one binary image representation. CTUDR is verified on a signal smoothing and classification task and compared with conventional techniques, such as the Moving Average, the Binomial, the Median, and the Savitzky Golay filters. Simulated EEG data with added white Gaussian noise is employed in the former, while cognitive conflict data obtained from a 3D object selection task is utilized in the latter. CTUDR outperforms its counterparts, scoring the best fitting error and correlation coefficient in signal smoothing while achieving the highest gain in Accuracy (0.7640%) and F-measure (0.7607%) when used as a smoothing filter for training data of EEGNet.

Accuracy Evaluation of Visible-Near Infrared Spectroscopy for Detecting Insect Damage in Acorns of Quercus acuta

Abstract This study aimed to test near-infrared spectroscopy to assess insect damage to oak acorns collected from a seed orchard of Quercus acuta in Jeju Island, Korea. A total of 550 acorns were sorted into 362 sound and 178 unsound (insect-damaged) acorns, followed by near-infrared spectroscopy. To minimize spectral data errors, preprocessing techniques such as first derivative, multiplicative scatter correction, standard normal variate, and Savitzky-Golay filter were applied, along with multivariate analysis methods like partial least squares. Then the model performance, including accuracy and precision, was evaluated using the Variable Importance in Projection. The near-infrared wavelength of the acorns showed strong absorption peaks at 660~720nm and a slight downward trend at 900~1000nm. The most effective model for distinguishing unsound acorns was Savitzky-Golay filtering treatment applied in the 400~1000nm range and used partial least squares, showing prediction accuracy of 86 % (p<0.05). The performance was significantly influenced by absorption points at 660~720nm and 960~1000nm, with the latter range believed to be affected by changes in moisture and carbohydrates due to insect damage. The former range showed lower classification capability due to chlorophyll and color variation but affected the model performance when used with near-infrared wavelength range. These findings can narrow down the scope of investigation for future research using wider wavelength ranges or multispectral analysis.

Integrating near-infrared hyperspectral imaging with machine learning and feature selection: Detecting adulteration of extra-virgin olive oil with lower-grade olive oils and hazelnut oil

Detecting adulteration in extra virgin olive oil (EVOO) is particularly challenging with oils of similar chemical composition. This study applies near-infrared hyperspectral imaging (NIR-HSI) and machine learning (ML) to detect EVOO adulteration with hazelnut, refined olive, and olive pomace oils at various concentrations (1%, 5%, 10%, 20%, 40%, and 100% m/m). Savitzky-Golay filtering, first and second derivatives, multiplicative scatter correction (MSC), standard normal variate (SNV), and their combinations were used to preprocess the spectral data, with Principal Component Analysis (PCA) reducing dimensionality. Classification was performed using Partial Least Squares-Discriminant Analysis (PLS-DA) and ML algorithms, including k-Nearest Neighbors (k-NN), Naïve Bayes, Random Forest (RF), Support Vector Machine (SVM), and Artificial Neural Networks (ANN). PLS-DA, k-NN, RF, SVM, NB, and ANN models achieved accuracy rates of 97.0–99.0%, 96.2–100%, 96.5–100%, 98.6–99.5%, 93.9–99.7%, and 99.2–100%, respectively, in discriminating between pure EVOO, adulterants, and adulterated oils. PLS-DA, RF, SVM, and ANN significantly outperformed Naïve Bayes (p < 0.05) in binary classification, with Matthews correlation coefficient (MCC) values exceeding 0.90. All the binary classifiers except Naïve Bayes, when coupled with SNV/MSC, Savitzky-Golay smoothing and derivatives, consistently achieved perfect scores (1.0) for accuracy, sensitivity, specificity, F1 score, precision, and MCC in distinguishing pure EVOO from adulterated oils. No significant differences (p > 0.05) in model performance were found between those using full spectra and those based on key variable selection. However, PLS-DA and ANN significantly outperformed k-NN, RF, and SVM (p < 0.05), with MCC values ranging from 0.95 to 1.00, indicating superior classification performance. These findings demonstrate that combining NIR-HSI with machine learning, along with key variable selection, potentially offers an effective, non-destructive solution for detecting adulteration in EVOO and combating fraud in the olive oil industry.

Design of multi-ensemble hybrid filtering approach for removal of heart sound from lung auscultations

Successful lung sound extraction from lung auscultations requires precise filters. Lung auscultations include heart and lung sounds. Therefore, the filter design should identify heart sound characteristics. These include periodicity, pitch, frequency, amplitude, etc. Auscultation acquisition sensors are inefficient, so these signals have noise. To get a clean auscultation signal, ambient noise, periodic noise, DC offsets, baseline errors, harmonic noise, etc. must be addressed separately. Data cleaning must maintain a high peak-signal-to-noise ratio without removing desirable signal information. Heart sound patterns are extracted from input auscultations using filter banks on these signals. After heart sound extraction, the output sound sample should only contain lung sounds. Still, heart sound harmonics corrupt output lung sound due to similarities between heart and lung sound patterns. This lowers lung-sound extraction quality and automatic lung-based disease identification efficiency levels. This article proposes a 2-level multi-ensemble filtering model with 43 filters that analyze 15 other parameters to denoise and extract lung sound from lung auscultations to eliminate these drawbacks. Combining LMS, NLMS, and RLS is used for denoising process. For heart sound identification, an ensemble of Savitzky-Golay, FIR equiripple, Butterworth, Chebyshev, Elliptic, and wavelet filters is used. This selective combination of filters improves PSNR by 20% compared to sole filter performance, while signal entropy, crest factor, root mean squared error, kurtosis, etc. also improves for different scenarios.

Hyperspectral identification of oil adulteration using machine learning techniques

Food adulteration is a global concern, drawing attention from safety authorities due to its potential health risks. Detecting and categorizing oil adulteration is crucial for consumer safety and food industry integrity. This research explores hyperspectral imaging (HSI) analysis to identify substandard oil adulteration at different stages. Using the non-destructive HSI Specim Fx 10 system, a method for precise and easy imaging-based fraud detection and classification was proposed. The 670 oil samples, including pure (Almond, Mustard, Coconut, Olive) and adulterated (Sunflower, Castor, Liquid Paraffin), were analyzed. The Savitzky-Golay filter preprocessed the images to remove noise and smooth spectral signatures. The oils were identified using various machine learning approaches, including Support Vector Machines, Logistic Regression, Linear Discriminant Analysis, Random Forests, Decision Trees, K-Nearest Neighbors, and Naïve Bayes with Linear Discriminant Analysis excelling in identification. Performance parameters, including precision, recall, F1-score, and overall accuracy, were calculated. The proposed method achieved a validation accuracy of 100%, outperforming numerous state-of-the-art approaches. This study introduces a robust pipeline for effective oil adulteration detection, offering a significant advancement in food safety and quality control.

By cyclists, for cyclists: Road grade and elevation estimation from crowd-sourced fitness application data.

Road grade or slope is a key factor for walking and cycling behavior and outcomes (influencing route, speed, energy, etc.). For this reason, the scarcity of precise road grade data presents a challenge for travel information and analysis. This paper examines the accuracy of using crowd-sourced GPS data from a fitness application to estimate roadway grade profiles, which can then be used to develop network-wide road grade datasets. We externally validate an elevation estimation method described by McKenzie and Janowicz using field surveying data, and then propose and evaluate modifications for estimation of road grade (which is more directly relevant than elevation for walking and cycling analysis). We find that a modest amount of crowd-sourced GPS data can be used to generate relatively accurate road grade estimates: better than commonly-used low-resolution elevation models, but not as accurate as high-resolution data derived from LiDAR (Light Detection and Ranging). We also find that the grade estimates are more reliable than the elevation estimates, relative to alternative data sources. The most accurate method to aggregate crowd-sourced GPS data builds a composite roadway grade profile using partition-around-medoid clustering of individual grade sequences, first smoothed with a Savitzky-Golay filter and cleaned with Density-Based Spatial Clustering of Applications with Noise (DBSCAN). Implementing this method with an average of 150 GPS traces per location yields a root mean square error (RMSE) of 1% road grade. The findings in this paper can be used to incorporate precise road grade information into street network datasets over a wide spatial scale, which is necessary for walking and cycling analysis that fully considers the physiological aspects of active transportation.

Temperature vegetation dryness index (TVDI) for drought monitoring in the Guangdong Province from 2000 to 2019.

Drought monitoring is crucial for assessing and mitigating the impacts of water scarcity on various sectors and ecosystems. Although traditional drought monitoring relies on soil moisture data, remote sensing technology has have significantly augmented the capabilities for drought monitoring. This study aims to evaluate the accuracy and applicability of two temperature vegetation drought indices (TVDI), TVDINDVI and TVDIEVI, constructed using the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI) vegetation indices for drought monitoring. Using Guangdong Province as a case, enhanced versions of these indices, developed through Savitzky-Golay filtering and terrain correction were employed. Additionally, Pearson correlation analysis and F-tests were utilized to determine the suitability of the Standardized Precipitation Index (SPI) and the Standardized Precipitation Evapotranspiration Index (SPEI) in correlation with TVDINDVI and TVDIEVI. The results show that TVDINDVI had more meteorological stations passing both significance test levels (P<0.001 and P<0.05) compared to TVDIEVI, and the average Pearson'R correlation coefficient was slightly higher than that of TVDIEVI, indicating that TVDINDVI responded better to drought in Guangdong Province. Our conclusion reveals that drought-prone regions in Guangdong Province are concentrated in the Leizhou Peninsula in southern Guangdong and the Pearl River Delta in central Guangdong. We also analyzed the phenomenon of winter-spring drought in Guangdong Province over the past 20 years. The area coverage of different drought levels was as follows: mild drought accounted for 42% to 64.6%, moderate drought accounted for 6.96% to 27.92%, and severe drought accounted for 0.002% to 1.84%. In 2003, the winter-spring drought in the entire province was the most severe, with a drought coverage rate of up to 84.2%, while in 2009, the drought area coverage was the lowest, at 49.02%. This study offers valuable insights the applicability of TVDI, and presents a viable methodology for drought monitoring in Guangdong Province, underlining its significance to agriculture, environmental conservation, and socio-economic facets in the region.

Dry season temperature and rainy season precipitation significantly affect the spatio-temporal pattern of rubber plantation phenology in Yunnan province.

The ongoing global warming trajectory poses extensive challenges to plant ecosystems, with rubber plantations particularly vulnerable due to their influence on not only the longevity of the growth cycle and rubber yield, but also the complex interplay of carbon, water, and energy exchanges between the forest canopy and atmosphere. However, the response mechanism of phenology in rubber plantations to climate change remains unclear. This study concentrates on sub-optimal environment rubber plantations in Yunnan province, Southwest China. Utilizing the Google Earth Engine (GEE) cloud platform, multi-source remote sensing images were synthesized at 8-day intervals with a spatial resolution of 30-meters. The Normalized Difference Vegetation Index (NDVI) time series was reconstructed using the Savitzky-Golay (S-G) filter, coupled with the application of the seasonal amplitude method to extract three crucial phenological indicators, namely the start of the growing season (SOS), the end of the growing season (EOS), and the length of the growing season (LOS). Linear regression method, Pearson correlation coefficient, multiple stepwise regression analysis were used to extract of the phenology trend and find the relationship between SOS, EOS and climate factors. The findings demonstrated that 1) the phenology of rubber plantations has undergone dynamic changes over the past two decades. Specifically, the SOS advanced by 9.4 days per decade (R2 = 0.42, p< 0.01), whereas the EOS was delayed by 3.8 days per decade (R2 = 0.35, p< 0.01). Additionally, the LOS was extended by 13.2 days per decade (R2 = 0.55, p< 0.01); 2) rubber phenology demonstrated a notable sensitivity to temperature fluctuations during the dry season and precipitation patterns during the rainy season. The SOS advanced 2.0 days (r =-0.19, p< 0.01) and the EOS advanced 2.8 days (r =-0.35, p< 0.01) for every 1°C increase in the cool-dry season. Whereas a 100 mm increase in rainy season precipitation caused the SOS to be delayed by 2.0 days (r = 0.24, p< 0.01), a 100 mm increase in hot-dry season precipitation caused the EOS to be advanced by 7.0 days (r =-0.28, p< 0.01); 3) rubber phenology displayed a legacy effect of preseason climate variations. Changes in temperature during the fourth preseason month and precipitation during the fourth and eleventh preseason months are predominantly responsible for the variation in SOS. Meanwhile, temperature changes during the second, fourth, and ninth preseason months are primarily responsible for the variation in EOS. The study aims to enhance our understanding of how rubber plantations respond to climate change in sub-optimal environments and provide valuable insights for sustainable rubber production management in the face of changing environmental conditions.

Denoising ECG Signals using Weighted Iterative UFIR Filtering

The electrocardiogram (ECG) holds paramount importance in diagnosing heart disease, and as it persists leading cause of global mortality. Over the past decades, diverse techniques have emerged for processing ECG signals, with denoising taking a prominent role in enhancing feature extraction. Nonetheless, achieving heightened accuracy remains an enduring challenge. In this study, we introduce an innovative approach involving the application of a weighted unbiased finite impulse response (UFIR) filter. Under the same noise conditions and in terms of the root mean square error (RMSE) and signal-to-noise ratio (SNR), our proposed method showcases worthy performance in comparison to the weighted Savitzky-Golay (SG) filter. This research contributes to the progressive evolution of ECG signal processing, offering the potential for more precise and dependable detection of cardiac diseases.

An Indoor Fire Detection Method Based on Multi-Sensor Fusion and a Lightweight Convolutional Neural Network.

Indoor fires pose significant threats in terms of casualties and economic losses globally. Thus, it is vital to accurately detect indoor fires at an early stage. To improve the accuracy of indoor fire detection for the resource-constrained embedded platform, an indoor fire detection method based on multi-sensor fusion and a lightweight convolutional neural network (CNN) is proposed. Firstly, the Savitzky-Golay (SG) filter is used to clean the three types of heterogeneous sensor data, then the cleaned sensor data are transformed by means of the Gramian Angular Field (GAF) method into matrices, which are finally integrated into a three-dimensional matrix. This preprocessing stage will preserve temporal dependency and enlarge the characteristics of time-series data. Therefore, we could reduce the number of blocks, channels and layers in the network, leading to a lightweight CNN for indoor fire detection. Furthermore, we use the Fire Dynamic Simulator (FDS) to simulate data for the training stage, enhancing the robustness of the network. The fire detection performance of the proposed method is verified through an experiment. It was found that the proposed method achieved an impressive accuracy of 99.1%, while the number of CNN parameters and the amount of computation is still small, which is more suitable for the resource-constrained embedded platform of an indoor fire detection system.

On the feasibility of Vis–NIR spectroscopy and machine learning for real time SARS-CoV-2 detection

The pandemic caused by Covid-19 is still present around the world. Despite advances in combating the disease, such as vaccine development, identifying infected individuals is still essential to optimize the control of human-to-human transmission of the virus. The main technique for detecting the virus is the RT-PCR method, which, despite its high relative cost, has a high accuracy in detecting the coronavirus. Given this, a method capable of performing the identification quickly, accurately, and inexpensively is necessary. Thus, this work aimed to analyze the feasibility of a new technique for identifying SARS-CoV-2 through the use of optical spectroscopy in the visible and near-infrared range (Vis–NIR) combined with machine learning algorithms. Spectral signals were obtained from nasopharyngeal swab samples previously analyzed using the RT-PCR method. The specimens were provided by the Molecular Diagnosis Laboratory of Covid-19 at Univasf. A total of 314 samples were analyzed, comprising 42 testing positive and 272 testing negative for Covid-19. Digital signal processing techniques, such as Savitzky–Golay filters and statistical methods were used to eliminate spurious elements from the original data and extract relevant features. Supervised machine learning algorithms such as SVM, Random Forest, and Naive Bayes classifiers were used to perform automatic sample identification. To evaluate the performance of the models, a 5-fold cross-validation technique was applied. With the proposed methodology, it was possible to achieve an accuracy of 75%, a sensitivity of 80%, and a specificity of 70%, in addition to an area under the ROC curve of 0.81, in the identification of nasopharyngeal swab samples from previously diagnosed individuals. From these results, it was possible to conclude that Vis–NIR spectroscopy is a promising, fast and relatively low cost technique to identify the SARS-CoV-2.

Denoising and R-Peak Detection in ECG Signals: A Performance Evaluation

An electrocardiogram (ECG) is a continuous electrical signal from the heart that is recorded to understand the activity and condition of the heart. A recorded ECG signal always follows a defined pattern for a normal heart condition. Variation in the normal ECG pattern can be seen in cases of numerous cardiac abnormalities. A recorded ECG is also affected by a number of noises and distortions, resulting in a low SNR. A variation in ECG pattern can lead to incorrect study and improper diagnosis of heart condition. Thus, to perform an efficient analysis, it is necessary to preprocess the ECG waveform. ECG preprocessing requires noise removal and analysis of necessary features needed to study cardiac activity. In this paper, ECG preprocessing is evaluated by using two noise removal techniques, i.e., finite and infinite impulse response. After this, the R-peaks are detected using discrete wavelet transform (DWT), maximal optimal DWT, principal component analysis and independent component analysis. A wavelet transform technique is further proposed using Savitzky-Golay filtering and DWT. The results obtained from the proposed methodology represent the best results compared to those of other methods explicated in this paper.

An Output-Only, Energy-Based, Damage Detection Method Using the Trend Lines of the Structural Acceleration Response

Using the trendlines of an acceleration response as a tool to decompose a structural response is a new topic that was proposed by authors in 2020. This paper provides a numerical/experimental investigation of using a Savitzky–Golay filter (SGF) in a method to calculate the trendline and decompose building acceleration responses when subjected to a seismic load. Hence, this paper proposes an output-only, energy-based, damage detection method in which the trend lines of a building’s structural acceleration responses are used to locate the damage. For this purpose, an adjusted SGF is utilized to calculate an especial trend line for each floor’s acceleration response of the building structural model. The energy of these trend lines is then calculated and normalized. Two damage indices are used, of which, the second one is being proposed for the first time in this paper. The accuracy of the proposed method is numerically and experimentally investigated using a five-floor building structural model subjected to white noise excitation through a shake table. The results prove that the proposed method is capable of accurately locating and quantifying structural damages with a severity of more than 10% in a noisy environment. In view that the proposed method locates the damage with no need of determining the structural modal properties or parameters, it can be categorized as an online and quick structural damage detection method.

Research on Denoising of GIS Ultra-High Frequency Partial Discharge Signal Based on VMD Combined with S-G Filter

Given the problem that it is easy to receive thermal noise interference from the electronic circuit and equipment circuit of the detection system in the current feature frequency detection of Gas Insulated Switchgear (GIS) equipment, this paper proposes an ultra-high frequency (UHF) signal noise reduction method based on variational mode decomposition (VMD) combined with Savitzky-Golay (S-G) filter and tests it through simulation. By using VMD combine with the S-G filter method, the signal-to-noise ratio (SNR) of signals can be effectively improved and the interference of white noise to signals can be reduced.

The Study of Properties Savitzky-Golay Polynomial Smoothing Filter for Electrocardiogram Signal Processing

Many types of processing techniques have been proposed to improve the performance of biomedical signal with noise. The Savitzky-Golay (SG) filters is one of the techniques used in filtering noise which can smoothen out the signal without much destroying its original properties. Despite their exceptional features they were rarely used so far in the ECG signal processing. The principle behind S-G filter is to obtain the appropriate Polynomial degree fitting order and frame size properties since the performance of filter mostly depends on them. Thus, the appropriate properties of S-G filter in noisy signal needs to be examined. In this study, combination between band-pass filter and S-G filter is implemented. The implementation has been applied S-G filter on the noisy ECG signal with different Signal to noise ratio and artefacts. The aim of this paper is the investigation of S-G filter properties in detail from the ECG signal processing aspect. The comparison of properties of S-G filter on ECG signal with different signal of noise ratio are also discussed. The parameters which provide the highest correlation coefficient are considered for filter design.

Characterization of Unplasticized Polyvinyl Chloride Windows by Confocal Raman Microspectroscopy and Chemometrics

In order to nondestructively and accurately identify unplasticized polyvinyl chloride windows, a classification method based on multi-feature algorithm selection modeling was developed. Confocal Raman microspectroscopy was used to obtain the spectral profiles of 150 samples from five brands. The differences in model recognition accuracy were compared among three preprocessing methods: Savitzky-Golay filtering, Hilbert transform, and wavelet transform. The best preprocessing method was selected, and the competitive adaptive reweighted sampling was used to extract feature wavelengths. Furthermore, a Bayesian classification model was constructed to classify and differentiate each sample. The results showed that confocal Raman microspectroscopy can reflect the differences in physicochemical information among different samples. Preprocessing can improve the model’s recognition accuracy, with wavelet transform (96%) > Hilbert transform (90%) > Savitzky-Golay filtering (76%) > untreated (72%). Wavelet transform can remove noise from spectral data without changing the peak region and its absorbance. Based on wavelet transform processing and competitive adaptive reweighted sampling (CARS) combined with Bayesian discriminant analysis, a 100% accurate classification of 150 samples was successfully achieved.

Analytical estimation of the signal to noise ratio efficiency in axion dark matter searches using a Savitzky-Golay filter

The signal to noise ratio efficiency ϵSNR in axion dark matter searches has been estimated using large-statistic simulation data reflecting the background information and the expected axion signal power obtained from a real experiment. This usually requires a lot of computing time even with the assistance of powerful computing resources. Employing a Savitzky-Golay filter for background subtraction, in this work, we estimated a fully analytical ϵSNR without relying on large-statistic simulation data, but only with an arbitrary axion mass and the relevant signal shape information. Hence, our work can provide ϵSNR using minimal computing time and resources prior to the acquisition of experimental data, without the detailed information that has to be obtained from real experiments. Axion haloscope searches have been observing the coincidence that the frequency independent scale factor ξ is approximately consistent with the ϵSNR. This was confirmed analytically in this work, when the window length of the Savitzky-Golay filter is reasonably wide enough, i.e., at least 5 times the signal window.

Three methods for determining respiratory waves from ECG (Part I)

In the diagnosis of many disease entities directly or indirectly related to disorders of respiratory parameters and heart disease, an important support would be to estimate the temporal changes in these parameters (most often respiratory wave (RW) and respiratory rate (RR)) on the basis the results of measurements of other physiological parameters of the patient. Such a possibility exists during ECG examination. The paper presents three methods for estimating RWand RR using ECG signal processing. The three procedures developed are shown: using Savitzky–Golay filtering (S-G), the ECG-Derived Respiration method (EDR) and the Respiratory Sinus Arrhythmia Analysis method (RSA). It must be clearly stated that the proposed methods are not designed to fully diagnose the patient’s respiratory function, but they can be applied to detect some conditions that are difficult to diagnose when performing an ECG, such as sleep-disordered breathing. The obtained results of the analysis were compared with those obtained from a dedicated measurement system developed by the authors. The second part of the paper will show the results of preliminary clinical verification of the developed analysis methods, taking into account the physiological parameters of the patient.