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Journal of Neuroscience Methods 170 (2008) 310–316

Influence of filters in the detrended fluctuation analysis of digitalelectroencephalographic data

Miguel Valencia a,∗, Julio Artieda a,b, Manuel Alegre a,b, Diego Maza c

a Center for Applied Medical Research (CIMA), University of Navarra, 31080 Pamplona, Spainb Neurophysiology Section, Clınica Universitaria de Navarra, University of Navarra, 31080 Pamplona, Spain

c Institute of Physics, University of Navarra, 31080 Pamplona, Spain

Received 25 November 2007; received in revised form 12 January 2008; accepted 15 January 2008

bstract

The technique named detrended fluctuation analysis (DFA) has been used to reveal the presence of long-range temporal correlations (LRTC)nd scaling behavior (SB) in electroencephalographic (EEG) recordings. The occurrence of these phenomena seems to be a salient characteristicf the healthy human brain and alterations in different pathologies has been described. Here we show how the filtering stages implemented in the

ystems for digital EEG influence the estimation of the DFA parameters used to characterize the brain signals. In consequence, we conclude thatt is important to consider these filtering effects before interpreting the results obtained from digital EEG recordings. 2008 Elsevier B.V. All rights reserved.

eywords: Detrended fluctuation analysis (DFA); Electroencephalogram (EEG); Long-range temporal correlations (LRTC); Filtering; Analog-to-digital conversion

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A/D); Scaling behavior (SB)

. Introduction

The human brain spontaneously generates neural oscilla-ions with large variability in frequency, amplitude, duration,nd recurrence. This apparently information-less activity haseen ignored for years. Recently, several studies have shown thatespite its apparent random temporal structure, baseline oscilla-ory activity is characterized by persistent long-range temporalorrelations (LRTC) and scaling behaviors (SB) that last for tensf seconds (Hwa and Ferree, 2002b, a; Linkenkaer-Hansen et al.,001).

The presence of LRTC – in the sense of slow power-law decayutocorrelations – can be associated to constancy preservation,ariability reduction and mostly adaptability in the systems. Inractical time series, the estimation of the autocorrelation func-ion (AFC) is limited at large values of time by the noise; making

t difficult to detect LRTC (Perazzo et al., 2004). Nevertheless,he LRTC can also be detected in the fluctuations of the timeeries. The detrended fluctuation analysis (DFA) was developed

∗ Corresponding author. Tel. +34 948 194700; fax: +34 948 194715.E-mail addresses: mvustarroz@unav.es (M. Valencia), jartieda@unav.es

J. Artieda), malegre@unav.es (M. Alegre), dmaza@unav.es (D. Maza).

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165-0270/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2008.01.010

ith this aim (Peng et al., 1994). This technique has provedo be well suited for quantifying correlations in non-stationaryignals, because long-range correlations – revealed by an ACFnalysis – can arise also as an ‘artifact’ of the ‘patchiness’ ofon-stationary data. The DFA was specifically developed to dif-erentiate between intrinsic fluctuations generated by complexystems and those caused by external or environmental stimulicting on the system (Peng et al., 1995a). Variations related toxternal stimuli are presumed to cause a local effect, whereasariations due to intrinsic dynamics of the system are expectedo exhibit long-range correlations (Seely and Macklem, 2004).

The DFA measures the variance of linearly detrended signalss a function of a window size, s. It represents a measure ofcale invariant behavior because it evaluates trends of all sizes,rends that exhibit fractal properties, i.e. with similar patternsf variation across multiple time scales (Seely and Macklem,004). The DFA computes an average fluctuation function F (s),hat can be often related to the window size by a power-law,(s) ∼ sα which defines a characteristic scaling exponent, α.his exponent provides a quantitative measure of the temporal

orrelations that exist in the time series. When signals presentifferent correlation properties for short versus long-temporalcales, the DFA is able to identify both regimes (Kantelhardt etl., 2001; Nagarajan and Kavasseri, 2005; Peng et al., 1995a). It

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M. Valencia et al. / Journal of Neur

etects a crossover at a scale sc separating regimes with differentcaling exponents, e.g. long-range correlations on small scales< sc and another type of correlations or uncorrelated behaviorn larger scales s > sc. For example, in the case of electrocar-iographic (ECG) signals, the DFA identifies two distinct linearegments separated by a crossover. These two different regimesould evidence the presence of two different mechanisms –ith different dynamical properties – that mediate to assure the

daptability of the cardiac rhythm. In patients with severe heartisease the adaptability of the heart is affected and as a result,ifferences in the LRTC has been described (Goldberger et al.,002; Peng et al., 1995b).

Influenced by the good results obtained for cardiac signals,he DFA analysis has given rise to many studies that havedentified characteristic crossovers and scaling differences inEG signals. The occurrence of LRTC and SB in EEG sig-als seems to be a characteristic of the healthy human brainnd has led to the elucidation of organization principles (Bak,996; Buzsaki, 2006). LRTC mediates as a (self-)organizingechanism that unifies highly complex processes that generateuctuations across different time scales. They feature one of theharacteristics of the healthy functioning brain: the adaptabilityr the capacity of the brain to respond to unpredictable stimuli.

Alterations in patients affected by Alzheimer’s disease (Pant al., 2004) or depression (Leistedt et al., 2007) have beenescribed. These studies were motivated by the discoveryf LRTC in the amplitudes of the alpha and beta rhythmsLinkenkaer-Hansen et al., 2001). Further studies have reportedts consistency across several days (Nikulin and Brismar,005), the influence of sensory stimuli (Linkenkaer-Hansent al., 2004), or additional deviations in the theta band ofepressed patients (Linkenkaer-Hansen et al., 2005). In epilep-ic patients, differences in the LRTC between epileptogenicnd non-epileptogenic hippocampus have also been describedParish et al., 2004). Large-scale neuronal networks depend oneural interactions both at synaptic and network levels. Abnor-alities in the complex set of regulatory mechanisms would

ecrease the LRTC and the observed alterations can be explaineds an expression of a global and non-specific modification in theynamics of the neuronal networks in the patients.

Most of these results have been obtained by applying directlyhe DFA over the digitized EEG signal. For a digitized signal,t can be demonstrated that the digitalization process does notesult in a loss of information nor it does introduce distortionsf the signal bandwidth is finite (Nyquist, 1928; Oppenheim andchafer, 1989; Shannon, 1949). As the EEG signal is a fairlylow (low-pass) signal, acquisition systems used to limit the EEGandwidth to a few tens or hundreds hertz (Rangayyan, 2002).n addition, it is also very common (and usually not reported) toancel low frequencies, because EEG systems often suffer fromery slow drifts that saturate the analog-to-digital (A/D) con-erter. These drifts can be associated to gradual changes in theuality of electrode contact to the skin, breathing movements, or

lectrode-wire displacements; but they could also reveal charac-eristics related to the brain dynamics (Vanhatalo et al., 2004).

The aim of the present study is to warn about the influencehat the filtering scheme used to record digital EEGs could have

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nce Methods 170 (2008) 310–316 311

ver the DFA results. Different filter configurations modify thecaling properties of the EEG signals to different extents, andhe parameters extracted by means of the DFA analysis couldesult in false or disturbed interpretations of real phenomena.

To analyze the influence of the filters in the performance of theFA measures, we studied the results obtained when applying

he DFA directly over real EEG recordings, in the same way asn previous reports (Hwa and Ferree, 2002a, b; Lee et al., 2004;eistedt et al., 2007; Pan et al., 2004; Parish et al., 2004; Shent al., 2003). To asses our findings, we simulated uncorrelatedoise and applied the same analysis directly over the simulatedignal.

. Materials and methods

.1. EEG acquisition system

The EEG acquisition system was composed by an ampli-cation module followed by an A/D converter that stored theigitized EEG in a personal computer.

Amplification and filtering were carried out by means of eightigh performance preamplifiers GRASS-IP511 (Astro-Med Inc.,raintree, MA, USA). This model is a general purpose ampli-er for the amplification of bioelectric signals from micro- andacro-electrodes. It provides different active high and low passlter configurations. Specifically, it offers nine selectable 2-ole (−12 dB/octave) high-pass filters at 0.01, 0.1, 0.3, 1, 3, 10,0, 100 and 300 Hz. Regarding the low-pass filters, six 4-pole−24 dB/octave) at 0.03, 0.1, 0.3, 1, 3 and 10 kHz are available.

switch-selectable notch filter for line removal (50–60 Hz) islso present.

The A/D conversion, signal simulation and recording wherearried out by means of the Spike2 software and a CEDower1401 A/D converter (Cambridge Electronic Design,ambridge, UK); the Power1401 is a high-performance datacquisition interface that records analog data, digital (events)nd marker information. Additionally, it can generate ana-og/digital outputs simultaneously for real-time, multi-taskingxperimental control paradigms.

.2. Human EEG recording

Three subjects took part in the study. At least 10 min of restingEG was obtained from each subject, recorded from Cz elec-

rode (according to the 10:20 International System) referred tone earlobe. The subjects were instructed to keep their eyes openooking at a fixed point during the recording. In the third patient,wo additional sessions were recorded with eyes closed, Oz inhe first; and Cz in the second one. The subjects were seated incomfortable armchair in a light-attenuated and magnetically

hielded room.The study was performed with the understanding and written

onsent of the subjects and with the approval of the local ethics

ommittee. In all the experiments, the same EEG signal wasassed across eight different amplifiers with the same amplifi-ation (10,000 ×) but different filter settings. We tested the 0.01,.1, 0.3, 1, 3, 10, 30 and 100 Hz cutoff frequencies for the high

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ass filters, while the low-pass remained fixed to 300 Hz andhe 50 Hz notch-filter disabled. This ensured that the differencesetween signals were only due to the filtering scheme settingsnd not to different EEG recordings. The eight channels wereampled with a 1000 Hz sampling frequency per channel. Aftercquisition, EEG recordings were reviewed in order to ensurehe absence of artifacts.

.3. Uncorrelated noise

To analyze the effects of the filtering scheme over signalsith known correlation properties we simulated an uncorre-

ated white noise. This noise was simulated by means of theandom number generator implemented in the Power1401. Theystem was set to generate pseudo-random sequences of 215 dif-erent levels with an amplitude of 50 mV. Then, as in the EEGxperiment, the signal was passed across the different GRASS-P511 amplifiers. The same low- and high-pass filter schemesnd sampling frequency as in the previous analysis were used.he amplification was set to 100×, and the notch-filter was alsoisabled.

.4. Detrended fluctuation analysis

In our study, we follow the method described by Peng etl. (1995a). According to this scheme, the calculation of theFA for a discrete time series {xi}, i = 1, . . . , N, involves sev-

ral steps. In the first step, the cumulated sum of the record isetermined:

(i) =i∑

k=1

xk − 〈x〉, i = 1, . . . , N (1)

he subtraction of the mean 〈x〉 is not compulsory since it isancelled by the detrending procedure in the third step.

In the second step, the cumulated sum Y (i) is cut into Ns ≡N/s] non-overlapping segments of equal length s. Since theecord length N needs not to be a multiple of the consideredime scale s, a short part at the end of the profile will remain in

ost cases.In the third step, the local trend for each segment is calculated

y means of a least-squares fit of the data. Then the detrendedime series for segment duration s is defined as the differenceetween the original time series and the fit:

Ys(j) = Y (j) − pv(j), v = 1, . . . , Ns,

j = [(v − 1)s] + 1, . . . , vs (2)

here pv(j) is the fitting polynomial in the v th segment. Linear,uadratic, cubic, or higher order polynomials can also be usedn the fitting procedure (DFA1, DFA2, DFA3 and higher orderFA). Since the detrending of the time series is done by the

ubtraction of the fits from the profile, these methods differ in

heir capability of eliminating trends in the data. In n th orderFA, trends of order n in Y (i), and of order n − 1 in the original

ecord are eliminated (Hu et al., 2001; Chen et al., 2002). Toest the robustness of our analysis against different polynomial

filS

ience Methods 170 (2008) 310–316

rends, we used two different orders for the polynomial fitting,and 2.In the fourth step, the variance of each of the Ns segments of

he detrended time series Ys(j) is calculated by averaging overll data points j in the v th segment.

2s (v) = 〈Y2

s (j)〉 = 1

s

s∑j=1

Y2s [(v − 1)s + j], (3)

Finally, by averaging over all segments and taking the squareoot, the DFA fluctuation function is obtained:

(s) =[

1

Ns

Ns∑v=1

F2s (v)

]1/2

, (4)

It is apparent that the variance will increase with increasinguration s of the segments. If the data {xi} are long-range power-aw correlated, the fluctuation function F (s) increase accordingo a power-law:

(s) ∝ sα, (5)

The DFA scaling exponent is extracted with linear regressionn double-logarithmic coordinates using a least-squares algo-ithm. A value of α = 0.5 characterizes the ideal case of anncorrelated signal (White noise), whereas 0.5 < α < 1 indi-ates power-law scaling behavior and the presence of temporalong-range correlations such that a large value (compared to theverage) is more likely to be followed by another large valuend vice versa. In contrast, 0 < α < 0.5 indicates a differentype of power-law correlation such that large and small valuesf the time series are more likely to alternate. The special casef α = 1 corresponds to 1/f noise, while periodic signals have= 0 for time scales larger than the period of repetition. For≥ 1, correlations exists but cease to be of a power-law form;= 1.5 indicates Brownian noise, the integration of the 1/f

oise (Peng et al., 1995a; Perazzo et al., 2004). In this sense,he exponent α can be interpreted as an indicator that describeshe “roughness” of the time series. The 1/f noise can be vieweds a “compromise” between the complete unpredictability ofhe White noise (very rough “landscape”) and the very smoothlandscape” of the Brownian noise.

. Results

.1. Presence of LRTC

In all experiments, the range of time scales in which the fluc-uation function F (s) showed a linear behavior – versus timecale of observation – varied with the filtering configuration.ecords with higher bandwidths presented broader ranges of

cales in which the relation F (s) ∼ sα held. These ranges pre-ented a decrease in their extent as the cut-off frequency wasncreased (see Figs. 1–3 ).

In the case of the open-eyes recordings, the most open con-guration (fc = 0.01 Hz) gives a straight line that ranges from

og10 s ∼ 0.5 to log10 s ∼ 5, revealing presence of LRTC andB for all the time-scales analyzed (see Fig. 1). Surprisingly,

M. Valencia et al. / Journal of Neuroscience Methods 170 (2008) 310–316 313

Fig. 1. Fluctuation function for the EEG recording from subject S3, Cz electrode,under open-eyes condition. Lines correspond to each one of the filtering schemess3m

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Fig. 3. Analysis of the uncorrelated noise: effects of the filtering scheme in therts

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tudied: (·) 0.01 Hz, (+) 0.1 Hz, (∗) 0.3 Hz, (�) 1 Hz, (♦) 3 Hz, (�) 10 Hz, ()0 Hz and (�) 100 Hz. The added dashed line (- - -) represents a guide with slope= 1.

or the other configurations the same EEG signal presents notne, but two different regions with different scaling regimes.he influence of the filtering scheme over the DFA results isvident as the extent of the scaling regions varies with filteringonfiguration.

In the closed-eyes experiment, the DFA is able to detect theffect of the alpha rhythm, which in this condition representscharacteristic scale of the EEG (see Fig. 2). This effect is

evealed by a smooth deviation from linearity in the log–log plott time windows related to the alpha-band rhythm (log10 s ∼ 2).

he influence of the filters is the same as in the open-eyesondition and some configurations disturb the detection ofhis real characteristic of the EEG signal. When using higherrders of polynomial fitting, the alpha rhythm characteristic

ig. 2. Analysis of the EEG recording from the Oz electrode for subject S3,losed-eyes condition. The effect of the alpha rhythm is detected at segmentizes s 2 as a soft deviation from the linear trend of the graph. Symbols arehe same as those of Fig. 1; slope of the dashed guide: m = 1.

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esults obtained with the DFA for uncorrelated noise. In this case, the slope ofhe dashed line is m = 0.5; the value of the scaling exponent for an uncorrelatedignal. Configurations are represented by the same symbols as those of Fig. 1.

ecomes more evident (more marked deviation from linearity),hile the influence of the filters is the same as in the previous

nalysis.For the simulated uncorrelated noise, the same effects as in

he real EEG are observed (Fig. 3). The same signal presentsifferent regions with SB depending on the filtering configura-ion.

.2. Analysis of crossovers

The splitting from one to two regimes of scaling behavioralls for an analysis of the crossover ordinates and their depen-ence on the parameters of the filtering stage.

The most intuitive method to estimate the crossover ordi-ates consists of splitting the linearized fluctuation functionlog10 F (s) ∼ α log10 s) into different segments, each of themorresponding to a “linear” part of the graph. Then, eachegment is approximated to a line by linear regression in double-ogarithmic coordinates using a least-squares algorithm. Thentersection of the approximated regressions, gives the positionf the crossover ordinate (see Fig. 4).

Although this approach is intuitively satisfying, it is neces-ary to define the extremes of the linear segments, which adds aubjective component to the analysis. Nevertheless, it should beoted that each filter cut-off frequency fc, is related to a charac-eristic segment length sfc , according to log10 sfc = log10 fs/fc;here fs stands for the selected sampling frequency (fs = 1000z). From these values (see Table 1, second row) and according

o the shape of the fluctuation functions (Figs. 1–3), it is possi-le to define two different “linear” regimes for the fluctuationunctions. The first region includes segments of lengths from the

inimum to lengths related to half a decade bellow the ordinate

elated to the filter cuttoff frequency, sfc . The second one com-rises segments from half a decade after the crossover ordinateo the end of the graph.

314 M. Valencia et al. / Journal of Neuroscience Methods 170 (2008) 310–316

Fig. 4. Extraction of the scaling exponents and crossover for two different filterconfigurations: (∗) 0.3 Hz and (♦) 3 Hz. Analysis carried out on the EEG fromsubject S3, Cz electrode, under the open-eyes condition. Dashed lines representlinear least-squares fits of the linear segments of the fluctuation functions. TheiWi

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Fig. 5. Representation of the detected crossover ordinates against the differentfilter cut-off frequencies. The sfc crossover ordinates related to the filter cuttofffrequencies (see text) are represented by the dashed line.

Table 2Values of the scaling exponents obtained for each analysis, filtering configurationand segment

fc (Hz) 0.01 0.1 0.3 1 3 10 30 100αS1Cz 1.14 1.11 1.15 1.17 1.04 1.03 0.98 0.86αS2Cz 1.29 1.31 1.28 1.14 1.19 1.13 1.27 0.68αS3Cz (open) 1.18 1.21 1.22 1.21 1.16 1.08 1.14 0.83αS3Oz (closed) 1.01 0.87 0.79 0.60 0.60 – – –αS3Cz (closed) 1.18 1.12 1.01 0.86 0.72 – – –αnoise 0.52 0.52 0.51 0.52 0.54 0.55 0.59 0.62

Only the values of the scaling exponents for the valid range of time scales aresis

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ntersection between adjusted lines marks the experimental crossover position.hile arrows denote the ordinate of the sfc scales. Triangles delimit the ranges

n which the fluctuation functions were fitted.

The comparison of the values of sfc with those obtainedrom the EEG segments and simulated noise, results in a com-lete correlation between the ordinates of the crossovers and thisheoretical estimation (see Fig. 5 and Table 1).

.3. Analysis of scale exponents

Once the regions in which F (s) presents linear behaviors haveeen defined, these segments are adjusted to a line using a least-quares algorithm by linear regression in double-logarithmicoordinates (see Fig. 4). The slope of the adjusted lines rep-esents the value of the scaling exponent (see Table 2).

Under the open-eyes condition, for thefc = 0.01 Hz settings,ll subjects present a scaling exponent α ∼ 1.2, but as the filter-ng schemes change, the bandwidth of the EEG signal is reduced,nd the set of scales with almost-zero α increase their extent.

It is easy to note how filters induce significant deviations

n the slope of the graph for long-temporal scales. The use of

ore restrictive filtering schemes does not only split a uniquecaling region into two different parts, but also alters the esti-

able 1osition of the ordinates related to the filter cuttoff frequencies sfci

, and ordinatesf the crossovers detected experimentally

ci(Hz) 0.01 0.1 0.3 1 3 10 30 100

fci5.00 4.00 3.52 3.00 2.52 2.00 1.52 1.00

S1Cz – 4.19 3.66 2.78 2.64 2.18 1.86 0.88

S2Cz – 3.75 3.39 3.04 2.48 2.00 1.32 0.99

S3Cz (open) – 4.02 3.31 2.89 2.48 2.01 1.42 0.95

S3Oz (closed) – 3.52 3.22 2.65 2.21 2.16 1.52 0.97

S3Cz (closed) – 3.81 3.36 2.76 2.27 1.89 1.50 1.00

noise – 3.64 3.18 2.68 2.22 1.72 1.26 1.086

t should be noted that for the first configuration (fc = 0.01 Hz), the fluctuationunction presented no evident crossover for the range of scales analyzed.

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hown (i.e. s ∈ [0.6, sf ci− 0.5]). For the closed-eyes condition, we avoided the

nfluence of the alpha rhythm by estimating the scaling exponents in the range∈ [2, sf ci

− 0.5].

ation of the scaling exponent (see Table 2). For example, inlosed-eyes experiment, in electrode Oz, the value of the scal-ng exponent decreases from α = 1.01 for fc = 0.01 Hz, to= 0.60 for fc = 1 Hz, what represents a decrement of 40% in

he estimated values.As expected, for the simulation of the uncorrelated noise the

caling exponent in the first segment is very close to α ≈ 0.5,hich corresponds to an uncorrelated signal. Nevertheless, the

xtent of the graph in which this value holds, decreases byncreasing the cut-off frequencies. In this case, the effect of theltering scheme is the same as for the EEG signals, but it shoulde noted that the bending in the fluctuation functions is lessarked (compared to the EEG signals) due to the lower slope

f the graphs (Fig. 3).

. Discussion

We have analyzed some methodological aspects of the DFAnalysis in the study of digital EEG recordings. We used a real

EG system to study real EEG signals and a simulated signalith known scaling properties. We have analyzed the influencef the filtering scheme over the parameters obtained with theFA analysis. As a result, we can state that the filters modify

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M. Valencia et al. / Journal of Neur

he parameters extracted with the DFA technique, and this facthould be considered when interpreting the results obtained fromigital EEG recordings.

Filters induce a spurious crossover in the DFA graph at aosition related to the filter cut-off frequencies; and more impor-antly, due to the finite width of the filter transition band, they alsoffect the estimation of the scaling exponents. We have demon-trated how these transition bands favor a decay in the slope ofhe fluctuation function F (s) before reaching lengths associatedo the filter cut-off frequency. This leads to an underestimationf the scale exponents used to characterize the properties of theEG; it is interesting to note how some filter transition bandsnderestimate the value of the scaling exponents in comparisonith those obtained for other configurations. For example, in

he extreme case of fc = 1 Hz, the estimated exponent is nearlyalf of the real exponent obtained for EEG signals α ∼ 1.1 (evenhough it has been extracted in the region theoretically out of thelter influence). These facts represent a clear example of arti-acts that could invalidate or lead to erroneous conclusions forreal world” data.

It should be stressed that we recorded only 1 channel at aime because we preferred to use the same EEG signal simulta-eously. We selected the Cz position because this is a commonite in almost all of the clinical procedures in which EEG record-ngs are involved. In addition, we also performed recordings inhe Cz and Oz positions under the closed-eyes condition. Asxpected the DFA was able to detect the influence of the alphahythm on the resting EEG dynamics. Nevertheless, the resultsere exposed can be generalized because the analysis under-aken does not depend on the statistical validation of the data,or in the position of recording, but on the settings of the EEGcquisition system.

We should also point out that in clinical routine EEG record-ngs, it is not usual to use filters with such extreme cutoff valuesfc ≥ 10), as they are to be used in the study of local field poten-ials or single-unit activities, but we have introduced them hereo illustrate their effect on the DFA technique.

Despite the important influence that the setup of the recordingystem seems to have over the performance of the DFA, someeports do not offer a description of the filtering scheme (Lee etl., 2004; Pan et al., 2004) or no care is taken for the influencef these parameters (Hwa and Ferree, 2002b, a; Leistedt et al.,007).

This is even more striking if we consider some papershat relate the spectral analysis to the DFA (Heneghan, 2000;obinson, 2003; Talkner and Weber, 2000). Although the DFA

s a technique specifically suited to analyze non-stationary sig-als (Chen et al., 2005; Echeverrıa et al., 2003; Goldberger et al.,000, 2002; Nagarajan and Kavasseri, 2005; Peng et al., 1994,995a), it can be demonstrated that under stationarity and lin-arity constrains, the DFA results are comparable to the onesbtained by means of spectral analysis techniques (Heneghan,000; Perazzo et al., 2004; Robinson, 2003; Talkner and Weber,

000). In that sense, it is evident that the filtering process weighshe spectral content of the signal and this affects the estimationf the scale exponent. Nevertheless, this effect is not taken intoccount very often.

G

nce Methods 170 (2008) 310–316 315

There are already some papers that study the influence of non-inear filters (applied digitally) over the DFA analysis (Chen etl., 2005), but to our knowledge, none of them account for theffects induced by the analog filtering process.

The DFA was originally proposed for the study of correlationroperties in DNA nucleotides (Peng et al., 1994) and extendedo heartbeat time series (Peng et al., 1995a), two different fieldshere the filtering of the time series does not make (in princi-le) much sense. Nevertheless, this technique has been used tonalyze many other physiological signals where the use of filter-ng techniques are mandatory. In the case of the EEG, first it isecessary to low pass the signal to avoid the aliasing effects, andhen to cancel the low frequencies that eventually could saturatehe amplifier of the A/D converter. Reducing the width of thepectral content benefits the quality of the recorded signal, buts it has been demonstrated here, it also alters the values of thestimated parameters.

Interestingly, fractal dynamics with fluctuations on manycales seems to represent the hallmark of healthy systems. Whensing the DFA, the scaling exponent determines the nature ofhe fluctuations (most pathologies are associated with either tootable or too disorganized fluctuations) and the position of therossover defines the ranges of scales in which these LRTC hold,o artifacts in the estimation of these parameters could lead torroneous diagnosis.

Commonly, EEG researchers neglect the effect of the filteringtages implemented in the recording systems. High pass filtersffect very low frequencies that are crucial in the DFA anal-sis because its features are extracted from long lasting timeindows, but additionally they will also influence the perfor-ance of other techniques that analyze long-range temporal

roperties of the time series. In that sense, this study may be con-idered a necessary warning for the neuroscientific communityhat expects to use these kinds of analyses in their research.

cknowledgement

This project was partially funded through the ”UTE projectIMA”.

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