Aperiodic Component Research Articles

Impact of sleep deprivation on aperiodic activity: a resting-state EEG study.

Sleep deprivation (SD) has been shown to have a negative impact on alertness, as evidenced by behavioral and electroencephalographic studies. Nevertheless, conventional fixed-bandwidth spectral analysis confused the aperiodic and periodic components, and ignored some important periodic parameters (i.e., center frequency, bandwidth). Here, based on a large open access dataset of SD, we employed a standardized process for multiple electrode analysis and group inference. We found that, compared to SC, the aperiodic offset shifted overall after SD, primarily in the occipital region. And this shift was associated with a reduction in subjective alertness. For periodic component, we did not found any power change in alpha rhythm, but there is an increase in bandwidth of alpha. And the increased regions distributed in the occipital and temporal lobes. These findings highlight the potential significance and value of aperiodic parameters in behavioral and electrophysiological researches.

Structural inequality and temporal brain dynamics across diverse samples.

Structural income inequality - the uneven income distribution across regions or countries - could affect brain structure and function, beyond individual differences. However, the impact of structural income inequality on the brain dynamics and the roles of demographics and cognition in these associations remains unexplored. Here, we assessed the impact of structural income inequality, as measured by the Gini coefficient on multiple EEG metrics, while considering the subject-level effects of demographic (age, sex, education) and cognitive factors. Resting-state EEG signals were collected from a diverse sample (countries=10; healthy individuals=1394 from Argentina, Brazil, Colombia, Chile, Cuba, Greece, Ireland, Italy, Turkey and United Kingdom). Complexity (fractal dimension, permutation entropy, Wiener entropy, spectral structure variability), power spectral and aperiodic components (1/f slope, knee, offset), as well as graph-theoretic measures were analysed. Despite variability in samples, data collection methods, and EEG acquisition parameters, structural inequality systematically predicted electrophysiological brain dynamics, proving to be a more crucial determinant of brain dynamics than individual-level factors. Complexity and aperiodic activity metrics captured better the effects of structural inequality on brain function. Following inequality, age and cognition emerged as the most influential predictors. The overall results provided convergent multimodal metrics of biologic embedding of structural income inequality characterised by less complex signals, increased random asynchronous neural activity, and reduced alpha and beta power, particularly over temporoposterior regions. These findings might challenge conventional neuroscience approaches that tend to overemphasise the influence of individual-level factors, while neglecting structural factors. Results pave the way for neuroscience-informed public policies aimed at tackling structural inequalities in diverse populations.

Implications of Aperiodic and Periodic EEG Components in Classification of Major Depressive Disorder from Source and Electrode Perspectives.

Electroencephalography (EEG) is useful for studying brain activity in major depressive disorder (MDD), particularly focusing on theta and alpha frequency bands via power spectral density (PSD). However, PSD-based analysis has often produced inconsistent results due to difficulties in distinguishing between periodic and aperiodic components of EEG signals. We analyzed EEG data from 114 young adults, including 74 healthy controls (HCs) and 40 MDD patients, assessing periodic and aperiodic components alongside conventional PSD at both source and electrode levels. Machine learning algorithms classified MDD versus HC based on these features. Sensor-level analysis showed stronger Hedge's g effect sizes for parietal theta and frontal alpha activity than source-level analysis. MDD individuals exhibited reduced theta and alpha activity relative to HC. Logistic regression-based classifications showed that periodic components slightly outperformed PSD, with the best results achieved by combining periodic and aperiodic features (AUC = 0.82). Strong negative correlations were found between reduced periodic parietal theta and frontal alpha activities and higher scores on the Beck Depression Inventory, particularly for the anhedonia subscale. This study emphasizes the superiority of sensor-level over source-level analysis for detecting MDD-related changes and highlights the value of incorporating both periodic and aperiodic components for a more refined understanding of depressive disorders.

Aperiodic Component Analysis in Quantification of Steady-State Visually Evoked Potentials.

In this study, we aimed to investigate whether and how the aperiodic component in electroencephalograms affects different quantitative processes of steady-state visually evoked potentials and the performance of corresponding brain-computer interfaces. We applied the Fitting Oscillations & One-Over-F method to parameterize power spectra as a combination of periodic oscillations and an aperiodic component. Electroencephalographic responses and system performance were measured and compared using four prevailing methods: power spectral density analysis, canonical correlation analysis, filter bank canonical correlation analysis and the state-of-the-art method, task discriminant component analysis. We found that controlling for the aperiodic component prominently downgraded the performance of brain-computer interfaces measured by canonical correlation analysis (94.9% to 82.8%), filter bank canonical correlation analysis (94.1% to 87.6%), and task discriminant component analysis (96.5% to 70.3%). However, it had almost no effect on that measured by power spectral density analysis (80.4% to 78.7%). This was accompanied by a differential aperiodic impact between power spectral density analysis and the other three methods on the differentiation of the target and non-target stimuli. The aperiodic component distinctly impacts the quantification of steady-state visually evoked potentials and the performance of corresponding brain-computer interfaces. Our work underscores the significance of taking into account the dynamic nature of aperiodic activities in research related to the quantification of steady-state visually evoked potentials. The source code for our approach is available at https://github.com/didi226/scut_ssvep_aperiod.

Differential effects of haloperidol on neural oscillations during wakefulness and sleep

The electrical activity of the brain, characterized by its frequency components, reflects a complex interplay between periodic (oscillatory) and aperiodic components. These components are associated with various neurophysiological processes, such as the excitation-inhibition balance (aperiodic activity) or interregional communication (oscillatory activity). However, we do not fully understand whether these components are truly independent or if different neuromodulators affect them in different ways. The dopaminergic system has a critical role for cognition and motivation, being a potential modulator of these power spectrum components. To improve our understanding of these questions, we investigated the differential effects of this system on these components using electrocorticogram recordings in cats, which show clear oscillations and aperiodic 1/f activity. Specifically, we focused on the effects of haloperidol (a D2 receptor antagonist) on oscillatory and aperiodic dynamics during wakefulness and sleep. By parameterizing the power spectrum into these two components, our findings reveal a robust modulation of oscillatory activity by the D2 receptor across the brain. Surprisingly, aperiodic activity was not significantly affected and exhibited inconsistent changes across the brain. This suggests a nuanced interplay between neuromodulation and the distinct components of brain oscillations, providing insights into the selective regulation of oscillatory dynamics in awake states.

An Oscillation Stability Analysis of a Direct-Driven Wind Power Grid-Connected System Considering Low Voltage Ride Though from an Energy Perspective

To solve the problem of the oscillation stability of direct-driven wind-powered grid-connected systems with a low-voltage crossing control, a method of oscillation stability analysis for these systems, based on interactive energy, is proposed in this paper. Firstly, a dynamic energy model of a direct-driven wind-powered grid-connected system is established, considering a low-voltage traverse control. Secondly, the energy is divided into four parts—the line parameter energy, current inner loop energy, PLL energy, and current inner loop–PLL interaction energy—and the conduction path of the energy during a low-voltage crossing is described. On this basis, the aperiodic components of each energy path are analyzed, the stability level of the system is quantified, the influence of the different control parameters on the interactive energy dissipation is deduced, the key interactive control links affecting the stability of the system are screened, and the influence rules of the parameters are expounded. Finally, a direct-driven wind-powered grid-connected system model is built on the Rt-lab platform, and it is verified by a simulation test. The results show that the interaction energy generated by the interaction of the current inner loop and phase-locked loop is a key factor affecting the stability of the direct-driven wind-powered grid-connected system. The simulation test parameters of the control group were adjusted as the current inner loop’s proportion parameter increased from 1.32 to 5.28, the current inner loop’s integral parameter increased from 4.48 to 6.42, the PLL’s proportion parameter decreased from 9.45 to 6.3, and the PLL’s integral parameter decreased from 50.25 to 40.2. Both the theoretical and experimental results show that increasing the current inner loop’s integral and proportion parameters can improve the stability level of the direct-driven wind-powered grid-connected system; reducing the phase-locked loop’s proportion and integral parameters can also improve the stability level of the grid-connected system.

Multiple Intrinsic Timescales Govern Distinct Brain States in Human Sleep.

Human sleep exhibits multiple, recurrent temporal regularities, ranging from circadian rhythms to sleep stage cycles and neuronal oscillations during nonrapid eye movement sleep. Moreover, recent evidence revealed a functional role of aperiodic activity, which reliably discriminates different sleep stages. Aperiodic activity is commonly defined as the spectral slope χ of the 1/frequency (1/fχ) decay function of the electrophysiological power spectrum. However, several lines of inquiry now indicate that the aperiodic component of the power spectrum might be better characterized by a superposition of several decay processes with associated timescales. Here, we determined multiple timescales, which jointly shape aperiodic activity using human intracranial electroencephalography. Across three independent studies (47 participants, 23 female), our results reveal that aperiodic activity reliably dissociated sleep stage-dependent dynamics in a regionally specific manner. A principled approach to parametrize aperiodic activity delineated several, spatially and state-specific timescales. Lastly, we employed pharmacological modulation by means of propofol anesthesia to disentangle state-invariant timescales that may reflect physical properties of the underlying neural population from state-specific timescales that likely constitute functional interactions. Collectively, these results establish the presence of multiple intrinsic timescales that define the electrophysiological power spectrum during distinct brain states.

Impact of transcranial electrical stimulation on simultaneous stereoelectroencephalography recordings: A randomized sham-controlled study

ObjectiveClinical exploitation of transcranial electrical stimulation for focal epilepsy treatment lacks quantification of the underlying neurophysiological changes. This study explores the immediate effects of transcranial alternating (tACS) and direct (tDCS) current stimulation on local and network brain activity using simultaneous stereoelectroencephalography (SEEG) recordings. MethodsPatients were randomized for personalized tACS (n = 5) or tDCS (n = 6). Active stimulation (20 min) was preceded by sham stimulation (20 min). Changes in interictal epileptiform discharges (IED), functional connectivity (FC) and power spectral density (PSD) were quantified against baseline. ResultsResults demonstrated variable responses. Spike rate decreased in 2/6 subjects following sham and tDCS, while 2/6 showed an increase. Alpha power and aperiodic PSD components generally increased during and after tDCS but decreased following tACS. FC changes varied among subjects and were detectable even during sham sessions. ConclusionsStrong variability suggests that tES does not have a univocal effect on immediate changes in IED or FC, possibly due to the single session format and challenges in affecting subcortical areas. SignificanceThis is the first study to examine intracranial FC changes during tACS and tDCS, highlighting the importance of sham comparisons and individual variability in tES response, offering valuable insights into its application for epilepsy treatment.

Generalized Slowing of Resting-State Neural Oscillations in People With Schizophrenia

BackgroundRecent interest in how neural oscillations reflect the flow of information through the brain has led to partitioning electroencephalography (EEG) recordings into periodic (i.e., oscillatory) and aperiodic (i.e., nonoscillatory) components. While both contribute to conventional measures of power within the frequencies that compose EEG recordings, the periodic aspect characterizes true oscillations, the speed of which is thought to be critical to efficient functioning of neural systems. Given evidence of EEG power abnormalities in schizophrenia (SCZ), we sought to determine whether the periodic aspect of EEG was aberrant in people with SCZ and could serve as a general measure of brain efficiency. MethodsResting-state EEGs were gathered from 104 participants with SCZ and 105 healthy control participants. We used the FOOOF toolbox to remove aperiodic neural activity. We computed the cross-correlation between power spectra for individual participants and the mean power spectrum for all participants to quantify the relative speed of neural oscillations. ResultsPeriodic activity in SCZ was shifted toward lower frequencies than control participants during eyes-closed rest. On average, participants with SCZ had a 0.55-Hz shift toward oscillatory slowing across the frequency spectrum that predicted worse perceptual reasoning. Slower neural oscillations were associated with weaker perceptual reasoning in SCZ. ConclusionsSlowed periodic activity at rest is evident in SCZ and may represent inefficient functioning of neural circuits as reflected in worse perceptual reasoning. A slower pace of neural oscillations may be a general limitation on the transmission of information within the brain.

A Novel Time-Frequency Parameterization Method for Oscillations in Specific Frequency Bands and Its Application on OPM-MEG.

Time-frequency parameterization for oscillations in specific frequency bands reflects the dynamic changes in the brain. It is related to cognitive behavior and diseases and has received significant attention in neuroscience. However, many studies do not consider the impact of the aperiodic noise and neural activity, including their time-varying fluctuations. Some studies are limited by the low resolution of the time-frequency spectrum and parameter-solved operation. Therefore, this paper proposes super-resolution time-frequency periodic parameterization of (transient) oscillation (STPPTO). STPPTO obtains a super-resolution time-frequency spectrum with Superlet transform. Then, the time-frequency representation of oscillations is obtained by removing the aperiodic component fitted in a time-resolved way. Finally, the definition of transient events is used to parameterize oscillations. The performance of this method is validated on simulated data and its reliability is demonstrated on magnetoencephalography. We show how it can be used to explore and analyze oscillatory activity under rhythmic stimulation.

Test-Retest Reliability of EEG Aperiodic Components in Resting and Mental Task States.

Aperiodic activity is derived from the electroencephalography (EEG) power spectrum and reflects changes in the slope and shifts of the broadband spectrum. Studies have shown inconsistent test-retest reliability of the aperiodic components. This study systematically measured how the test-retest reliability of the aperiodic components was affected by data duration (1, 2, 3, 4, and 5min), states (resting with eyes closed, resting with eyes open, performing mental arithmetic, recalling the events of the day, and mentally singing songs), and methods (the Fitting Oscillations and One-Over-F (FOOOF) and Linear Mixed-Effects Regression (LMER)) at both short (90-min) and long (one-month) intervals. The results showed that aperiodic components had fair, good, or excellent test-retest reliability (ranging from 0.53 to 0.91) at both short and long intervals. It is recommended that better reliability of the aperiodic components be obtained using data durations longer than 3min, the resting state with eyes closed, the mental arithmetic task state, and the LMER method.

Developmental trajectories of EEG aperiodic and periodic components in children 2–44 months of age

The development of neural circuits has long-lasting effects on brain function, yet our understanding of early circuit development in humans remains limited. Here, periodic EEG power features and aperiodic components were examined from longitudinal EEGs collected from 592 healthy 2–44 month-old infants, revealing age-dependent nonlinear changes suggestive of distinct milestones in early brain maturation. Developmental changes in periodic peaks include (1) the presence and then absence of a 9-10 Hz alpha peak between 2-6 months, (2) nonlinear changes in high beta peaks (20-30 Hz) between 4-18 months, and (3) the emergence of a low beta peak (12-20 Hz) in some infants after six months of age. We hypothesized that the emergence of the low beta peak may reflect maturation of thalamocortical network development. Infant anesthesia studies observe that GABA-modulating anesthetics do not induce thalamocortical mediated frontal alpha coherence until 10-12 months of age. Using a small cohort of infants (n = 23) with EEG before and during GABA-modulating anesthesia, we provide preliminary evidence that infants with a low beta peak have higher anesthesia-induced alpha coherence compared to those without a low beta peak.

Aperiodic component of EEG power spectrum and cognitive performance are modulated by education in aging

Recent studies have shown a growing interest in the so-called “aperiodic” component of the EEG power spectrum, which describes the overall trend of the whole spectrum with a linear or exponential function. In the field of brain aging, this aperiodic component is associated both with age-related changes and performance on cognitive tasks. This study aims to elucidate the potential role of education in moderating the relationship between resting-state EEG features (including aperiodic component) and cognitive performance in aging. N = 179 healthy participants of the “Leipzig Study for Mind–Body-Emotion Interactions” (LEMON) dataset were divided into three groups based on age and education. Older adults exhibited lower exponent, offset (i.e. measures of aperiodic component), and Individual Alpha Peak Frequency (IAPF) as compared to younger adults. Moreover, visual attention and working memory were differently associated with the aperiodic component depending on education: in older adults with high education, higher exponent predicted slower processing speed and less working memory capacity, while an opposite trend was found in those with low education. While further investigation is needed, this study shows the potential modulatory role of education in the relationship between the aperiodic component of the EEG power spectrum and aging cognition.

Excitation/Inhibition balance relates to cognitive function and gene expression in temporal lobe epilepsy: a high density EEG assessment with aperiodic exponent.

Patients with epilepsy are characterized by a dysregulation of excitation/inhibition balance (E/I). The assessment of E/I may inform clinicians during the diagnosis and therapy management, even though it is rarely performed. An accessible measure of the E/I of the brain represents a clinically relevant feature. Here, we exploited the exponent of the aperiodic component of the power spectrum of the electroencephalography (EEG) signal, as a non-invasive and cost-effective proxy of the E/I balance. We recorded resting-state activity with high-density EEG from 67 patients with temporal lobe epilepsy and 35 controls. We extracted the exponent of the aperiodic fit of the power spectrum from source-reconstructed EEG and tested differences between patients with epilepsy and controls. Spearman's correlation was performed between the exponent and clinical variables (age of onset, epilepsy duration and neuropsychology) and cortical expression of epilepsy-related genes derived from the Allen Human Brain Atlas. Patients with temporal lobe epilepsy showed a significantly larger exponent, corresponding to inhibition-directed E/I balance, in bilateral frontal and temporal regions. Lower E/I in the left entorhinal and bilateral dorsolateral prefrontal cortices corresponded to a lower performance of short-term verbal memory. Limited to patients with temporal lobe epilepsy, we detected a significant correlation between the exponent and the cortical expression of GABRA1, GRIN2A, GABRD, GABRG2, KCNA2 and PDYN genes. EEG aperiodic exponent maps the E/I balance non-invasively in patients with epilepsy and reveals a close relationship between altered E/I patterns, cognition and genetics.

Resting state EEG in young children with Tuberous Sclerosis Complex.

Tuberous Sclerosis Complex (TSC) manifests behaviorally with features of autism, epilepsy, and intellectual disability. Resting state electroencephalography (EEG) offers a window into neural oscillatory activity and may serve as an intermediate biomarker between gene expression and behavioral manifestations. Such a biomarker could be useful in clinical trials as an endpoint or predictor of treatment response. However, seizures and antiepileptic medications also affect resting neural oscillatory activity and could undermine the utility of resting state EEG features as biomarkers in neurodevelopmental disorders such as TSC. This paper compares resting state EEG features in a cross-sectional cohort of young children with TSC (n=49, ages 12-37 months) to 49 age- and sex-matched typically developing controls. Within children with TSC, associations were examined between resting state EEG features, seizure severity composite score, and use of GABA agonists. Compared to matched typically developing controls, children with TSC showed significantly greater alpha and beta power in permutation cluster analyses iterated across a broad frequency range (2-50Hz). Children with TSC also showed significantly greater aperiodic offset after power spectra were parameterized using SpecParam into aperiodic and periodic components. Within children with TSC, greater seizure severity was significantly related to increased periodic peak beta power. Use of GABA agonists was also independently and significantly associated with increased periodic peak beta power; the interaction between seizure severity and GABA agonist use had no significant effect on peak beta power. The elevated peak beta power observed in children with TSC compared to matched typically developing controls may be driven by both seizures and GABA agonist use. It is recommended to collect seizure and mediation data alongside EEG data for clinical trials. These results highlight the challenge of using resting state EEG features as biomarkers in trials with neurodevelopmental disabilities when epilepsy and anti-epileptic medication are common.

Advanced qEEG analyses discriminate between dementia subtypes

BackgroundDementia is caused by neurodegenerative conditions and characterized by cognitive decline. Diagnostic accuracy for dementia subtypes, such as Alzheimer’s Disease (AD), Dementia with Lewy Bodies (DLB) and Parkinson’s Disease with dementia (PDD), remains challenging. MethodsHere, different methods of quantitative electroencephalography (qEEG) analyses were employed to assess their effectiveness in distinguishing dementia subtypes from healthy controls under eyes closed (EC) and eyes open (EO) conditions. ResultsClassic Fast-Fourier Transform (FFT) and autoregressive (AR) power analyses differentiated between all conditions for the 4–8 Hz theta range. Only individuals with dementia with Lewy Bodies (DLB) differed from healthy subjects for the wider 4–15 Hz frequency range, encompassing the actual dominant frequency of all individuals. FFT results for this range yielded wider significant discriminators vs AR, also detecting differences between AD and DLB. Analyses of the inclusive dominant / peak frequency range (4–15 Hz) indicated slowing and reduced variability, also discriminating between synucleinopathies vs controls and AD. Dissociation of periodic oscillations and aperiodic components of AR spectra using Fitting-Oscillations-&-One-Over-F (FOOOF) modelling delivered a reliable and subtype-specific slowing of brain oscillatory peaks during EC and EO for all groups. Distinct and robust differences were particularly strong for aperiodic parameters, suggesting their potential diagnostic power in detecting specific changes resulting from age and cognitive status. ConclusionOur findings indicate that qEEG methods can reliably detect dementia subtypes. Spectral analyses comprising an integrated, multi-parameter EEG approach discriminating between periodic and aperiodic components under EC and EO conditions may enhance diagnostic accuracy in the future.

Subthalamic nucleus input-output dynamics are correlated with Parkinson’s burden and treatment efficacy

The subthalamic nucleus (STN) is pivotal in basal ganglia function in health and disease. Micro-electrode recordings of >25,000 recording sites from 146 Parkinson’s patients undergoing deep brain stimulation (DBS) allowed differentiation between subthalamic input, represented by local field potential (LFP), and output, reflected in spike discharge rate (SPK). As with many natural systems, STN neuronal activity exhibits power-law dynamics characterized by the exponent α. We, therefore, dissected STN data into aperiodic and periodic components using the Fitting Oscillations & One Over F (FOOOF) tool. STN LFP showed significantly higher aperiodic exponents than SPK. Additionally, SPK beta oscillations demonstrated a downward frequency shift compared to LFP. Finally, the STN aperiodic and spiking parameters explained a significant fraction of the variance of the burden and treatment efficacy of Parkinson’s disease. The unique STN input-output dynamics may clarify its role in Parkinson’s physiology and can be utilized in closed-loop DBS therapy.

Signal Decomposition for Monitoring Systems of Processes

This article is devoted to the problem of signal decomposition into periodic and aperiodic components. According to the proposed approach, there is no need to evaluate the aperiodic component as a difference between the total signal of its periodic components. This research aims to create a general analytical approach that combines the Fourier and Maclaurin series methodologies into a single comprehensive series. As a result, analytical expressions for determining deposition coefficients were established for an aperiodic signal with a monoharmonic overlay. Recurrence relations were established to determine the coefficients of this series. These relations allow direct integrations of the obtained values of integrals to be avoided. The evaluated numerical values of the coefficients are also presented graphically and tabulated. It was proven that the values of these coefficients are universal numbers since they do not depend on the period/frequency of oscillations. The reliability of the proposed approach was confirmed by the fact that the evaluated coefficients are equal to the Fourier series coefficients in the case of a periodic signal. Also, for an aperiodic signal, these coefficients were reduced to the coefficients of the Maclaurin series. The usability of the proposed generalized analytical approach for signal decomposition is for control and monitoring systems of processes.

Aperiodic and periodic components of oscillatory brain activity in relation to cognition and symptoms in pediatric ADHD

Abstract Children with attention-deficit/hyperactivity disorder show deficits in processing speed, as well as aberrant neural oscillations, including both periodic (oscillatory) and aperiodic (1/f-like) activity, reflecting the pattern of power across frequencies. Both components were suggested as underlying neural mechanisms of cognitive dysfunctions in attention-deficit/hyperactivity disorder. Here, we examined differences in processing speed and resting-state-Electroencephalogram neural oscillations and their associations between 6- and 12-year-old children with (n = 33) and without (n = 33) attention-deficit/hyperactivity disorder. Spectral analyses of the resting-state EEG signal using fast Fourier transform revealed increased power in fronto-central theta and beta oscillations for the attention-deficit/hyperactivity disorder group, but no differences in the theta/beta ratio. Using the parameterization method, we found a higher aperiodic exponent, which has been suggested to reflect lower neuronal excitation-inhibition, in the attention-deficit/hyperactivity disorder group. While fast Fourier transform–based theta power correlated with clinical symptoms for the attention-deficit/hyperactivity disorder group only, the aperiodic exponent was negatively correlated with processing speed across the entire sample. Finally, the aperiodic exponent was correlated with fast Fourier transform–based beta power. These results highlight the different and complementary contribution of periodic and aperiodic components of the neural spectrum as metrics for evaluation of processing speed in attention-deficit/hyperactivity disorder. Future studies should further clarify the roles of periodic and aperiodic components in additional cognitive functions and in relation to clinical status.

On the question of determining the location of a short circuit on a power transmission line

An algorithm for eliminating aperiodic components from short circuit (SC) currents is proposed. The algorithm is implemented by computer technology and allows you to determine the location of a short circuit and phase loss in 0.5 - 0.6 milliseconds. During such a time interval, saturation of the magnetic circuits of current transformers (CTs) does not occur, and the processors receive undistorted information from the CTs. To implement the algorithm, four measurements of instantaneous current values, separated by equal time intervals (sampling intervals), are sufficient. Elimination of aperiodic components increases the accuracy of determining the location of the fault. The algorithm can be used to determine the location of phase failure, and in digital relay protection based on measuring currents and voltages.