Signal Artifacts Research Articles

The importance of ocular artifact removal in single-trial ERP analysis: The case of the N250 in face learning

ObjectiveSingle-trial event-related potentials (ERPs) offer fine-grained information about the trajectories of the neurocognitive processes but are highly sensitive to any artifacts in the EEG signal. The primary aim of this study was to assess the impact of ocular artifact removal on the single-trial N250 ERP analysis of face learning in individual participants. MethodsWe present a detailed description of our research-grade EEG hardware setup and a highly reproducible code (https://osf.io/aqhmn/) for generating time series of single-trial N250 ERP amplitudes and precise identification of a changepoint between face memory trace acquisition and maintenance. Ocular artifacts were removed using a new semi-automatic approach with only one hyperparameter based on the correlation between EEG components from independent component analysis (ICA) and the EOG signal. ResultsResults from the simulation study showed that our ocular artifact filtration decreased the average RMSE by half and achieved the highest increase of SNR among all the compared methods. It decreased standard deviations and improved the fit of the broken-line regression models for all participants by 25% ± 17% (min. 2%, max. 63%). Conclusions and significanceOcular artifact filtration had a substantial positive impact on the regression modeling of single-trial ERP amplitudes. Lack of ocular artifact removal can drastically distort the conclusions about the face learning process from single-trial N250 ERP experiments for individual participants. The changepoint locations changed for 13 out of 15 participants. This is the first published analysis of time series of single-trial N250 ERP amplitudes in face learning.

Subject-Dependent Artifact Removal for Enhancing Motor Imagery Classifier Performance under Poor Skills.

The Electroencephalography (EEG)-based motor imagery (MI) paradigm is one of the most studied technologies for Brain-Computer Interface (BCI) development. Still, the low Signal-to-Noise Ratio (SNR) poses a challenge when constructing EEG-based BCI systems. Moreover, the non-stationary and nonlinear signal issues, the low-spatial data resolution, and the inter- and intra-subject variability hamper the extraction of discriminant features. Indeed, subjects with poor motor skills have difficulties in practicing MI tasks against low SNR scenarios. Here, we propose a subject-dependent preprocessing approach that includes the well-known Surface Laplacian Filtering and Independent Component Analysis algorithms to remove signal artifacts based on the MI performance. In addition, power- and phase-based functional connectivity measures are studied to extract relevant and interpretable patterns and identify subjects of inefficency. As a result, our proposal, Subject-dependent Artifact Removal (SD-AR), improves the MI classification performance in subjects with poor motor skills. Consequently, electrooculography and volume-conduction EEG artifacts are mitigated within a functional connectivity feature-extraction strategy, which favors the classification performance of a straightforward linear classifier.

A Biometric Authentication Technique Using Smartphone Fingertip Photoplethysmography Signals

Biometric Authentication (BA) is the process by which physiological measurements can be used to identify a specific person. BA has been implemented in various applications such as financial transactions, data privacy, and access control. Photoplethysmography (PPG) signals can be acquired from devices such as smartphones, smartwatches, or web cameras, which allow biometric signals to be readily captured. In this paper, we developed a BA classifier method for smart devices, which first reduces motion and noise artifacts (MNAs) in raw PPG signals, and then identifies subjects using the MNA-reduced PPG signals. Specifically, our BA classifier algorithm adopts an ensemble bagged trees (EBT) classifier with 16 PPG signal features from time and frequency domains. In the BA context, false positive (FP) and false negative (FN) rates are very important measurements to be considered. Acceptable FP and FN values were obtained. Experimental results show that our EBT-based BA algorithm achieved accuracy levels of 98.0% and 95.0%. Also, equal error rates (EER) measurements accomplished acceptable values of 2.42% and 5.90%.

Design and Implementation of Hybrid Techniques and DA-based Reconfigurable FIR Filter Design for Noise Removal in EEG Signals on FPGA

Virtual Reality (VR) technology assists physically challenged personnel in their daily routine activities. The evolution of technology has enhanced the critical activities of people who use wheelchairs by extracting features through electroencephalogram (EEG) and promoting options for their choice for decision-making on their own. During extraction of EEG, signal artifacts may mislead the decision-making environment. Hence noise has to be removed with help of an FIR filter for accuracy. In this context utilization of finite impulse response (FIR) filters are so vital hence filters are incorporated with the hidden Markov model (HMM) and Gaussian mixture model (GMM) and supervised machine learning architecture of multirate support vector machine (SVM). The proposed EEG-based diagnosis system is a fully automated audio announcement system. The entire environment has been developed by Verilog HDL and MATLAB. Validated on Artix-7 FPGA development board and synthesized with Vivado Design Suite 2018.1. Obtained results exhibit an enhancement of 32% of signal-to-noise ratio (SNR),7% of mean square error (MSE), and 69% of abnormality recognition.

Clenching-Related Motion Artifacts in Functional Near-Infrared Spectroscopy in the Auditory Cortex.

Functional near-infrared spectroscopy (fNIRS), a non-invasive optical neuroimaging technique, has demonstrated its great potential in monitoring cerebral activity as an alternative to functional magnetic resonance imaging (fMRI) in research and clinical usage. fNIRS has seen increasing applications in studying the auditory cortex in healthy subjects and cochlear implant users. However, fNIRS is susceptible to motion artifacts, especially those related to jaw movement, which can affect fNIRS signals in speech and auditory tasks. This study aimed to investigate the motion artifacts related to jaw movements including clenching, speaking, swallowing, and sniffing in a group of human subjects, and test whether our previously established denoising algorithm namely PCA-GLM can reduce the motion artifacts. Our results have shown that the jaw movements introduced artifacts that resemble task-evoked activations and that the PCA-GLM method effectively reduced the motion artifacts due to the clenching movements. The preliminary results of the present study underline the importance of the removal of the jaw-movement-related artifacts in fNIRS signals and suggest the efficacy of our PCA-GLM method in reducing the motion artifacts. Clinical Relevance- This work studies the motion artifacts due to jaw movements that frequently occur in speech perception and production tasks and validates the efficacy of an established denoising algorithm which benefits fNIRS studies on auditory and language functions.

Muscle Artifact Removal in Single-Channel Electrocardiograms using Temporal Convolutional Networks.

The electrocardiogram (ECG) is a vital diagnostic tool used in many health applications. In practice, interference by muscle artifacts is very common and may significantly complicate interpretation of the ECG waveform. In this work we investigate the removal of muscle artifacts in single-channel ECG signals using neural network models. To this end, we compare two neural network architectures which were previously used for ECG denoising and propose a novel third method based on the ConvTasNet. The neural networks are trained on simulated data using artificial mixtures of single-channel ECG (lead II) and surface EMG signals taken from publicly available datasets. ECG data were sampled from the MIT-BIH Arrhythmia and the PTB-XL database. The former provides recordings of ambulatory ECGs while the latter contains a large variety of cardiac pathologies recorded in a clinical setting. The muscle artifacts were sampled from the MIT-BIH Noise Stress Test database and the TaiChi database. In the past, most denoising methods were only tested on the two smaller MIT-BIH datasets. In this work, we report performances on larger datasets and thus provide stronger evidence for a clinical use-case. We also report out-of distribution performance of the three methods by switching the ECG dataset between training and test. The herein investigated variant of the ConvTasNet substantially reduces interference by muscle artifacts, outperforms state-of-the-art methods and thus, may support clinical decision making.

Visual Object Recognition From Single-Trial EEG Signals Using Machine Learning Wrapper Techniques.

Responses of the human brain to different visual stimuli elicit specific patterns in electroencephalography (EEG) signals. It is confirmed that by analyzing these patterns, we can recognize the category of the visited objects. However, high levels of noise and artifacts in EEG signals and the discrepancies between the recorded data from different subjects in visual object recognition task make classification of cognitive states of subjects a serious challenge. In this research, we present a framework for evaluating machine learning and wrapper channel selection algorithms used for classifying single-trial EEG signals recorded in response to photographic stimuli. It is shown that by correctly mapping the entire EEG data space to informative feature spaces (IFS), the performance of the classification methods can improve significantly. Results outperform the state-of-the-art results and confirm efficiency of the proposed feature selection methods in capturing the most informative EEG channels. This can help to achieve high separability of object categories in single-trial visual object recognition task.

CACHET-CADB: A Contextualized Ambulatory Electrocardiography Arrhythmia Dataset.

ECG is a non-invasive tool for arrhythmia detection. In recent years, wearable ECG-based ambulatory arrhythmia monitoring has gained increasing attention. However, arrhythmia detection algorithms trained on existing public arrhythmia databases show higher FPR when applied to such ambulatory ECG recordings. It is primarily because the existing public databases are relatively clean as they are recorded using clinical-grade ECG devices in controlled clinical environments. They may not represent the signal quality and artifacts present in ambulatory patient-operated ECG. To help build and evaluate arrhythmia detection algorithms that can work on wearable ECG from free-living conditions, we present the design and development of the CACHET-CADB, a multi-site contextualized ECG database from free-living conditions. The CACHET-CADB is subpart of the REAFEL study, which aims at reaching the frail elderly patient to optimize the diagnosis of atrial fibrillation. In contrast to the existing databases, along with the ECG, CACHET-CADB also provides the continuous recording of patients' contextual data such as activities, body positions, movement accelerations, symptoms, stress level, and sleep quality. These contextual data can aid in improving the machine/deep learning-based automated arrhythmia detection algorithms on patient-operated wearable ECG. Currently, CACHET-CADB has 259 days of contextualized ECG recordings from 24 patients and 1,602 manually annotated 10 s heart-rhythm samples. The length of the ECG records in the CACHET-CADB varies from 24 h to 3 weeks. The patient's ambulatory context information (activities, movement acceleration, body position, etc.) is extracted for every 10 s interval cumulatively. From the analysis, nearly 11% of the ECG data in the database is found to be noisy. A software toolkit for the use of the CACHET-CADB is also provided.

SRI-EEG: State-Based Recurrent Imputation for EEG Artifact Correction.

Electroencephalogram (EEG) signals are often used as an input modality for Brain Computer Interfaces (BCIs). While EEG signals can be beneficial for numerous types of interaction scenarios in the real world, high levels of noise limits their usage to strictly noise-controlled environments such as a research laboratory. Even in a controlled environment, EEG is susceptible to noise, particularly from user motion, making it highly challenging to use EEG, and consequently BCI, as a ubiquitous user interaction modality. In this work, we address the EEG noise/artifact correction problem. Our goal is to detect physiological artifacts in EEG signal and automatically replace the detected artifacts with imputed values to enable robust EEG sensing overall requiring significantly reduced manual effort than is usual. We present a novel EEG state-based imputation model built upon a recurrent neural network, which we call SRI-EEG, and evaluate the proposed method on three publicly available EEG datasets. From quantitative and qualitative comparisons with six conventional and neural network based approaches, we demonstrate that our method achieves comparable performance to the state-of-the-art methods on the EEG artifact correction task.

Enhancing the accuracy of shock advisory algorithms in automated external defibrillators during ongoing cardiopulmonary resuscitation using a deep convolutional Encoder-Decoder filtering model

Survival from out-of-hospital cardiac arrests (OHCA) depends on an accurate defibrillatory shock decision during cardiopulmonary resuscitation (CPR). Since chest compressions induce severe motion artifact in the electrocardiogram (ECG), current automatic external defibrillators (AEDs) instruct the user not to perform CPR during the rhythm analysis period. However, performing continuous CPR is vital and dramatically increases the chance of survival. Hence, we demonstrate a novel application of a deep convolutional neural network encoder-decoder (CNNED) method to suppress CPR artifact in near real-time, using only ECG data. The encoder portion of the CNNED uses the magnitude and phase contents derived via time-varying spectral analysis to learn distinct features that are representative of both the ECG signal and CPR artifact. The decoder portion takes the results from the encoder and reconstructs what is perceived as the motion artifact-removed ECG data. These procedures are done via a multitude of training of the CNNED using many different arrhythmias contaminated with CPR. In this study, CPR-contaminated ECGs were generated by combining clean ECGs with 52 different CPR artifacts. ECG data from CUDB, VFDB, SDDB, and AFDB datasets which belong to the Physionet’s Physiobank archive were used to create the training set containing 14-second ECG segments. The performance of the proposed CNNED was evaluated on a separate test set comprised of 23,816 CPR-contaminated 14-second ECG segments from 458 subjects. The results were evaluated by three metrics: signal-to-noise ratio (SNR), correlation coefficient, and accuracy of Defibtech’s AED shock advisory algorithm (SAA). CNNED resulted in an increase of the mean SNR value from −3 dB to 7.5 dB and 7.1 dB for shockable and non-shockable rhythms, respectively. 80.85% of the filtered shockable and 74.13% of the filtered non-shockable ECG data were highly correlated (>0.7) with the artifact-free ECG; these values were only 13.30% and 12.71% for CPR-contaminated shockable and non-shockable, respectively, without our filtering approach. Comparing results of Defibtech’s AED SAA before and after applying CNNED on the CPR-contaminated ECG, the specificity improved from 96.21% to 99.14% for normal sinus rhythm, and from 88.5% to 96.45% for other non-shockable rhythms. The sensitivity of shockable detection also increased from 67.68% to 90.90% for ventricular fibrillation, and from 62.71% to 82.26% for ventricular tachycardia. These results indicate continuous and accurate AED rhythm analysis without stoppage of CPR, using only ECG data.

In-person vs video hookup instructions: a comparison of home sleep apnea testing quality.

The high prevalence of obstructive sleep apnea (OSA) in the general population makes diagnosing OSA a high priority. Typically, patients receive in-person instructions to hook up the home sleep apnea test devices. Using recorded video instructions would save health care personnel time and improve access to OSA diagnostics for patients in remote areas. The aim of this study was to compare the quality of home sleep apnea test recordings when using in-person and video hookup instructions in a randomized study. A total of 100 patients aged 18 to 70 years with suspected OSA were randomized to receive either in-person or video hookup instructions for the Nox T3 device (Nox Medical, Reykjavik, Iceland). The overall quality of the resulting sleep studies was analyzed by determining the number of technically invalid studies. The recording quality of 4 sensors (pulse oximeter, nasal cannula, thorax and abdominal respiratory inductance plethysmography belts) was assessed by checking for signal artifacts. No significant difference was found between the 2 groups in any quality index. Only 1 (2%) and 2 (3.9%) sleep studies were technically invalid in the in-person and video instructions group, respectively. The average ± standard deviation recording quality of the 4 sensors combined was 94.8% ± 13.6% for the in-person and 96.0% ± 11.0% for the video instructions group. This study found no difference in home sleep apnea test recording quality between the 2 groups. Video hookup instructions are therefore viable and an important step toward a telemedicine-based way of diagnosing OSA. Horne AF, Olafsdottir KA, Arnardottir ES. In-person vs video hookup instructions: a comparison of home sleep apnea testing quality. J Clin Sleep Med. 2022;18(8):2069-2074.

50/60 Hz Power Grid Noise as a Skin Contact Measure of Textile ECG Electrodes

The electrocardiogram (ECG) is one of the most commonly measured biosignals. In particular, textile electrodes allow for the measuring of long-term ECG without skin irritation or other discomforts for the patient. Such textile electrodes, however, usually suffer from insufficient or unreliable skin contact. Thus, developing textile electrodes is impeded by the often-complicated differentiation between signal artifacts due to moving and breathing and artifacts related to unreliable skin contact. Here, we suggest a simple method of using 50/60 Hz power grid noise to evaluate the skin contact of different textile electrodes in comparison with commercial glued electrodes. We use this method to show the drying of wetted skin under an embroidered electrode as well as sweating of the originally dry skin under a coated electrode with high water vapor resistance.

PO-1614 Quantification of MRI signal artifacts from titanium intracavitary brachytherapy applicator

PO-1614 Quantification of MRI signal artifacts from titanium intracavitary brachytherapy applicator

Hybrid optical parametrically-oscillating emitter at 1930\xa0nm for volumetric photoacoustic imaging of water content

Water plays a vital role in biological metabolism and it would be essential to trace the water content non-invasively, such as leveraging the vibrational absorption peak of the O–H bond. However, due to the lack of an efficient laser source, it was challenging to image the water content in the deep tissue with micron-level spatial resolution. To address this problem, we develop a high-power hybrid optical parametrically-oscillating emitter (HOPE) at 1930 nm, at which the vibrational absorption peak of the O–H bond locates. The maximum pulse energy is over 1.74 μJ with a pulse repetition rate of 50 kHz and a pulse width of 15 ns. We employ this laser source in the optical-resolution photoacoustic microscopy (OR-PAM) system to image the water content in the phantom and the biological tissue in vitro. Our 1930-nm OR-PAM could map the water content in the complex tissue environment at high spatial resolution, deep penetration depth, improved sensitivity, and suppressed artifact signal of the lipid.

Getting the nod: Pediatric head motion in a transdiagnostic sample during movie- and resting-state fMRI.

Head motion continues to be a major problem in fMRI research, particularly in developmental studies where an inverse relationship exists between head motion and age. Despite multifaceted and costly efforts to mitigate motion and motion-related signal artifact, few studies have characterized in-scanner head motion itself. This study leverages a large transdiagnostic public dataset (N = 1388, age 5-21y, The Healthy Brain Network Biobank) to characterize pediatric head motion in space, frequency, and time. We focus on practical aspects of head motion that could impact future study design, including comparing motion across groups (low, medium, and high movers), across conditions (movie-watching and rest), and between males and females. Analyses showed that in all conditions, high movers exhibited a different pattern of motion than low and medium movers that was dominated by x-rotation, and z- and y-translation. High motion spikes (>0.3mm) from all participants also showed this pitch-z-y pattern. Problematic head motion is thus composed of a single type of biomechanical motion, which we infer to be a nodding movement, providing a focused target for motion reduction strategies. A second type of motion was evident via spectral analysis of raw displacement data. This was observed in low and medium movers and was consistent with respiration rates. We consider this to be a baseline of motion best targeted in data preprocessing. Further, we found that males moved more than, but not differently from, females. Significant cross-condition differences in head motion were found. Movies had lower mean motion, and especially in high movers, movie-watching reduced within-run linear increases in head motion (i.e., temporal drift). Finally, we used intersubject correlations of framewise displacement (FD-ISCs) to assess for stimulus-correlated motion trends. Subject motion was more correlated in movie than rest, and 8 out of top 10 FD-ISC windows had FD below the mean. Possible reasons and future implications of these findings are discussed.

A Dual-Modal Single-Antibody Plasmonic Spectro-Immunoassay for Detection of Small Molecules.

Small molecules play a pivotal role in regulating physiological processes and serve as biomarkers to uncover pathological conditions and the effects of therapeutic treatments. However, it remains a significant challenge to detect small molecules given the size as compared to macromolecules. Recently, the newly emerging plasmonic immunoassays based on surface-enhanced Raman scattering (SERS) offer great promise to deliver extraordinary sensitivity. Nevertheless, they are limited by the intrinsic SERS intensity fluctuations associated with the SERS uncertainty principle. The single transducer that relies on the intensity change is also prone to false signals. Additionally, the prevailing sandwich immunoassay format proves less effective towards detecting small molecules. To circumvent these critical issues, a dual-modal single-antibody approach that synergizes both the intensity and shift of the peak-based immunoassay with Raman enhancement, coined as the INSPIRE assay, is developed for small molecules detection. With two independent transduction mechanisms, it allows better prediction of analyte concentration and attenuation of signal artifacts, providing a new and robust strategy for molecular analysis. With a proof-of-concept demonstration for detection of free T4 and testosterone in serum matrix, the authors envision that the INSPIRE assay could be expanded for a wide spectrum of applications in biomedical diagnosis, discovery of new biopharmaceuticals, food safety, and environmental monitoring.

Heart Rate Estimation Algorithm Based on Normalized Least Mean Square combining Complete Ensemble Empirical Mode Decomposition with Adaptive Noise

Aiming at the difficulty of extracting heart rate due to the relative movement between human body and acquisition equipment, this paper proposes a Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDA) based on Normalized Least Mean Square (NLMS) adaptive filtering combined with fully adaptive noise sets for heart rate estimation. Firstly, an adaptive filter was used to filter the motion artifacts in the original signal by taking the triaxial acceleration signal as the reference signal. Then, the PPG signal was decomposed by CEEMDAN to obtain a series of Intrinsic Modal Functions (IMF) from high to low frequency. The Permutation Entropy (PE) criterion was used to determine the threshold range of the signal, so as to filter out the high-frequency noise and baseline drift. The results show that the Pearson correlation coefficient between the computed heart rate of PPG signal after noise reduction and the standard heart rate based on ECG signal is 0.742, and the average absolute error percentage is 6.08%, which indicates that the proposed method can accurately calculate the heart rate in the exercise state, and is beneficial to human physiological monitoring under the exercise state.

Transcriptome diversity is a systematic source of variation in RNA-sequencing data.

RNA sequencing has been widely used as an essential tool to probe gene expression. While standard practices have been established to analyze RNA-seq data, it is still challenging to interpret and remove artifactual signals. Several biological and technical factors such as sex, age, batches, and sequencing technology have been found to bias these estimates. Probabilistic estimation of expression residuals (PEER), which infers broad variance components in gene expression measurements, has been used to account for some systematic effects, but it has remained challenging to interpret these PEER factors. Here we show that transcriptome diversity-a simple metric based on Shannon entropy-explains a large portion of variability in gene expression and is the strongest known factor encoded in PEER factors. We then show that transcriptome diversity has significant associations with multiple technical and biological variables across diverse organisms and datasets. In sum, transcriptome diversity provides a simple explanation for a major source of variation in both gene expression estimates and PEER covariates.

PPGMotion: Model-based detection of motion artifacts in photoplethysmography signals

Photoplethysmography (PPG) is used widely in health wearables to monitor biomarkers like heart rate. However, motion activities degrade the quality of the measured PPG signal, thereby reducing the accuracy of heart-rate estimation. Existing state-of-the-art methods for motion detection rely on the semi-periodic structure of PPG to detect the aperiodic motion artifacts, thereby failing in scenarios when motion contamination tends to be periodic. We propose a novel technique, PPGMotion, for detecting all types of motion artifacts in PPG signals with high accuracy, without the need for any reference motion signals. Our approach relies on the morphological structure of the artifact-free PPG signal. We compare our method against some classical methods on one synthetic and four real datasets – dataset (1) and (2) are obtained from finger pulse-oximeter under motion activities, dataset (3) and (4) are obtained from a wearable smartwatch. We show that for the synthetic dataset, the performance of PPGMotion is significantly better than existing work as the contaminated PPG tends to become periodic, with an increase in sensitivity of at least 20% over state-of-the-art methods. For real data, PPGMotion achieves similar performance for random motion artifact detection as the classical methods but performs significantly better when motion tends to be periodic, with at least 10% increase in sensitivity in detecting motion artifacts in datasets (2), (3), and (4).

Preeminently Robust Neural PPG Denoiser

Photoplethysmography (PPG) is a simple and cost-efficient technique that effectively measures cardiovascular response by detecting blood volume changes in a noninvasive manner. A practical challenge in the use of PPGs in real-world applications is noise reduction. PPG signals are likely to be compromised by various types of noise, such as scattering or motion artifacts, and removing such compounding noises using a monotonous method is not easy. To this end, this paper proposes a neural PPG denoiser that can robustly remove multiple types of noise from a PPG signal. By casting the noise reduction problem into a signal restoration approach, we aim to achieve a solid performance in the reduction of different noise types using a single neural denoiser built upon transformer-based deep generative models. Using this proposed method, we conducted the experiments on the noise reduction of a PPG signal synthetically contaminated with five types of noise. Following this, we performed a comparative study using six different noise reduction algorithms, each of which is known to be the best model for each noise. Evaluation results of the peak signal-to-noise ratio (PSNR) show that the neural PPG denoiser is superior in three out of five noise types to the performance of conventional noise reduction algorithms. The salt-and-pepper noise type showed the best performance, with the PSNR of the neural PPG denoiser being 36.6080, and the PSNRs of the other methods were 19.8160 and 32.8234. The Poisson noise type performed the worst, showing a PSNR of 33.0090; the PSNRs of other methods were 35.1822 and 33.4795, respectively. Thereafter, an experiment to recover a signal synthesized with two or more of the five noise types was conducted. When the number of mixed noises was two, three, four, and five, the PSNRs were 29.2759, 27.8759, 26.5608, and 25.9402, respectively. Finally, an experiment to recover motion artifacts was also conducted. The synthesized motion artifact signal was created by synthesizing only a certain ratio of the total signal length. As a result of the motion artifact signal restoration, the PSNRs were 25.2872, 22.8240, 21.2901, and 19.9577 at 30%, 50%, 70%, and 90% motion artifact ratios, respectively. In the three experiments conducted, the neural PPG denoiser showed that various types of noise were effectively removed. This proposal contributes to the universal denoising of continuous PPG signals and can be further expanded to denoise continuous signals in the general domain.