Two Sides of the Same Coin: ERP and Wavelet Analyses of Visual Potentials Evoked and Induced by Task-Relevant Faces

New analysis techniques of the electroencephalogram (EEG) such as wavelet analysis open the possibility to address questions that may largely improve our understanding of the EEG and clarify its relation with related potentials (ER Ps). Three issues were addressed. 1) To what extent can early ERERP components be described as transient evoked oscillations in specific frequency bands? 2) Total EEG power (TP) after a stimulus consists of pre-stimulus baseline power (BP), evoked power (EP), and induced power (IP), but what are their respective contributions? 3) The Phase Reset model proposes that BP predicts EP, while the evoked model holds that BP is unrelated to EP; which model is the most valid one? EEG results on NoGo trials for 123 individuals that took part in an experiment with emotional facial expressions were examined by computing ERPs and by performing wavelet analyses on the raw EEG and on ER Ps. After performing several multiple regression analyses, we obtained the following answers. First, the P1, N1, and P2 components can by and large be described as transient oscillations in the α and θ bands. Secondly, it appears possible to estimate the separate contributions of EP, BP, and IP to TP, and importantly, the contribution of IP is mostly larger than that of EP. Finally, no strong support was obtained for either the Phase Reset or the Evoked model. Recent models are discussed that may better explain the relation between raw EEG and ERPs.

raw EEG changes upon stimulus presentation, as the alpha rhythm (~8-12 Hz) strongly reduces after a stimulus and is often replaced by the more high-frequent beta rhythm (~13-20 Hz). Obviously, this activity shortly before stimulus onset is mostly not visible in ERPs due to cancellation, nevertheless, this pre-stimulus baseline activity may have a crucial impact on the observed ERPs (e.g., see Fellinger, Klimesch, Gruber, Freunberger, & Doppelmayr, 2011;Gruber et al., 2014;Klimesch, 2011). Time-frequency analyses enable us to determine the presence of oscillatory patterns in different frequency bands over time.
Thus, with wavelet analyses, it can be established whether oscillatory activity in a specific frequency band, often expressed in power (squared amplitude), increases or decreases relative to a certain event.
The goal of the current paper is to increase our understanding of early stimulus-related EEG activity by combining both approaches in different ways. Three closely related issues will be addressed. The first issue concerns the question to what extent observed ERP components can be understood as the summation of transient evoked oscillations in specific frequency bands. For example, can the early visual P1 and N1 components (e.g., see Klimesch, 2011;Klimesch et al., 2004) be understood as the peak and trough of an evoked (or Phase Reset, see below) alpha oscillation (i.e., alpha-ringing), or are these two ERP components related to different frequency bands? The second issue relates to the question whether the ERP approach may not lead to a serious underestimation of stimulus-related activity (e.g., see Makeig, Debener, Onton, & Delorme, 2004). By performing wavelet analyses on both the raw EEG and ERPs, we may be able to determine the contribution of evoked (stimulus-locked) and induced activity (not phase-locked but stimulus-related activity) to overall observed activity, and therefore may assess whether a significant amount of information is lost. A third issue concerns the origin of the ERP. If ERP components can be described as a summation of transient evoked oscillations in various frequency bands, is it then possibly the case that these evoked oscillations are related to pre-stimulus baseline activity? For example, a prominent model (i.e., the Phase Reset model) states that ERPs origi-nate from a phase-reset of ongoing oscillations (Başar, 1999; see already Savers, Beagley, & Henshall, 1974). If this view is correct then one might argue that ERPs are more indicative of the state of an individual rather than that they reflect different processing stages of these stimuli.
The general approach in this paper is to address the aforementioned issues by employing multiple linear regressions, which will allow us to determine the presence and the strength of the relation between the different relevant variables.

ERP Components Described as the Sum of Evoked Oscillations in Specific Frequency Bands
The first issue may be rephrased as the extent to which the amplitude of the ERP within a specific time window Δt can be described as a linear lower theta (θ 1 ), middle theta (θ 2 ), upper theta (θ 3 ), lower alpha (α 1 ), upper alpha (α 2 ), lower beta (β 1 ), and upper beta (β 2 ). An implication of the choice for these frequency bands is that a part of the ERP may be left unexplained. This contribution, which is most likely related to power in the delta (δ) band, may be estimated by including a constant in the regression analyses. As individual differences in estimated power may be very large and its distribution will be skewed, we computed the logarithm (log 10 ) of the estimated power values and used the transformed data for the regression analyses (e.g., see Koopman, Wouters, & Krijzer, 1996). In these specific regression analyses, we employed a step-in step-out approach, which implies that only those predictors are included that show a significant contribution.

Total Power Decomposed in Evoked, Baseline, and Induced Power
The second issue concerns the extent to which overall stimulus-related activity is due to evoked and induced activity. If the contribution of induced activity is very large, then focusing solely on ERPs as an index of stimulus-related processing is maybe too limited (e.g., see Buszáki, 2006;Makeig et al., 2004) as a substantial part of relevant activity is ignored. Here, we adopted an approach related to the research by Hanslmayr et al. (2007). The idea is that overall activity or total power (TP) within a specific time window Δt, which can be separated in different frequency bands (f i ; i = 1 to n), is a linear function of evoked The regression coefficients a i and b i specify the contribution of EP and

The Relation Between Pre-Stimulus Baseline Power and Evoked Power
The third issue to be addressed concerns the relation between pre-stimulus oscillations (i.e., pre-stimulus baseline activity) and evoked oscillatory activity, which may describe (see issue 1) the different exogenous ERP components. Multiple studies have tried to test the Phase Reset model (Başar, 1999;Savers et al., 1974). This model states that ERPs are actually the result of a phase reset of ongoing pre-stimulus oscillations at stimulus onset while the overall power in various frequency bands is thought to remain the same (e.g., see Makeig et al., 2004Makeig et al., , 2002. Several ideas have been proposed that may account for the presence of a phase reset at stimulus onset. For example, Burgess (2012) proposed the Firefly model of synchronization, which relates phase synchronization in specific frequency bands to an increase in neuronal communication triggered by an internal or external event. Klimesch, Sauseng, Hanslmayr, Gruber, and Freunberger (2007) proposed that stimuli may induce an event-related phase reorganization (ERPR) that plays a crucial role in the timing of neural processes. An alternative view, also pointed out by Başar (1999), may be based on the idea that the onset of an event induces a resonance of ongoing oscillations, which may actually depend on their phase at stimulus onset. To address the third issue, we used a comparable approach as before. Now, the idea is that EP for a specific frequency band f i within a specific time window Δt may be a linear function of induced power in the pre-stimulus baseline (BP) and a constant CP(f i )Δt, which explains changes in EP that cannot be described by BP.
The regression coefficient d i describes the extent to which BP predicts EP. The relation between the variables can again be determined by performing a multiple linear regression analysis and including a constant.
If the data reveal that the relation between EP and BP is very small or

Participants
One hundred and thirty participants took part in the experiment, who were recruited from the student population of several universities in

Stimuli and Procedure
The set of stimuli consisted of 240 of Ekman and Friesen's (1976) colored pictures of emotional facial expressions, which included angry, sad, happy, and neutral faces. Pictures were taken from 27 individuals (18 males).
Each trial started with a grey background (38 cd/m²) being presented for 1,500 ms. Subsequently, the relevant stimulus (a picture with a specific emotional expression) was presented in the center. Stimulus presentation ended after a response was given or after 500 ms, whichever came first. The size of all stimuli was 9.3º × 11.7º.
In three different blocks, participants were asked to press a response key with their preferred index finger as quickly and accurately as possible when they detected the go stimulus. The go stimulus varied per block, being either an angry, happy, or sad face. Before the start of each block, participants were informed which category required a response.
The three blocks of 240 trials each contained 120 go trials (angry-go; happy-go; sad-go) and 120 nogo trials composed of 40 neutral trials and two sets of 40 angry, happy, or sad trials depending on the type of block. In the following, these blocks are indicated as the Angry, Happy, and Sad blocks, which refers to the stimulus that required a response.
The order of the trials was randomized and the order of the blocks was counterbalanced. The duration of the task was approximately 25 min.

Data Analysis
Our interest here concerned the EEG data. Therefore, we did not focus on the acquired behavioral data.

EEG data
EEG was analyzed using Brain Vision Analyzer (Version 2.0.1.3931; Brain Products GmbH, Munich, Germany). The raw EEG data were first filtered by a Butterworth Zero Phase filter with a low cutoff of 0.16 Hz, and a high cutoff of 40 Hz. Next, ICA (Independent Component Analysis) was employed to extract signals that were considered as having a non-cortical origin (e.g., being due to blinks, saccades, muscle activity, and heart rate). Subsequently, a time window was selected from -800 until 1,850 ms relative to the markers that signaled the presentation of the facial expressions. A baseline correction of -100 to 0 ms was applied. Trials with artefacts (gradient criterion: 50 μV/ms; min-max criterion: -/+ 150 μV; low activity criterion: 0.5 μV per 100 ms) were removed. Next, nogo trials for each block were selected for the EEG analyses, which we chose to avoid possible interference from movement-related activity. Next, two different EEG analyses were performed for the nogo trials in the three separate blocks (Happy, Angry, Sad).
In the first analysis, we initially determined the nogo ERPs per individual by averaging across all nogo trials, separately per block.
Subsequently, a wavelet analysis (a complex Morlet with Gabor normalization, c = 5) was applied on the individual ERPs, which allows us to estimate EP in different frequency bands related to the nogo stimuli.
We extracted the power (in μV 2 ) of seven frequency bands, starting from the lower theta to the upper beta band, which were separated in seven logarithmic steps (see also Van  In the second analysis, we performed wavelet analyses with the same parameter settings as above but now directly on the raw EEG.
Thus, analyses were performed on the same trials but before averaging them. This implies that we included both evoked and induced power.
Next, an average was created, which can be considered as an estimate of TP. Subsequently, the averaged TP for each band was determined for the aforementioned 20 ms time windows, all with the same parameter settings as in the other analyses. Additionally, we estimated BP in the various frequency bands for the interval from -500 to -200 ms relative to stimulus onset.
The logarithm (log10) was computed for all obtained power values.
These transformed values were used for all statistical analyses that were performed with IBM SPSS statistics (version 23).

MultiplE linEar rEGrEssion
To estimate to what extent the proposed relations in equations 1, 2, and 3 hold, three different multiple linear regression models were tested for the nogo stimuli in all three blocks. In the first regression model (related to Equation 1), the amplitude of the ERP within a specific 20ms time window at O2 was the dependent variable, and EP in the seven frequency bands for the same time window plus a constant were used as the predictor variables. In this case, a stepwise multiple linear regression analysis was carried out. To minimize statistical Type I errors, the critical p in -value was set at 0.05/(number of predictors). The number of predictors amounted to 8 (constant, plus the coefficients for the θ 1 up to the β 2 bands). The exclusion criterion p out was set at 2 × p in , which is the standard setting for this criterion (p in <= 0.00625, p out > 0.0125).
The regression analyses were performed for those intervals in which clear ERP components were observed.
In the second regression model (related to Equation 2), TP within a specific time window was the dependent variable, and EP, BP, and a constant (an estimate of the remaining IP) were used as the predictor variables. As we examined 13 time windows, seven frequency bands, and included three predictors, we had to minimize Type I errors.
The criterion of significance for at least two successive time windows was employed (see Van der Lubbe et al., 2014). This implies that the critical p value for two successive time windows amounted to 0.014 In the third regression model (related to Equation 3), EP within a specific time window was used as the dependent variable, while BP and a constant were used as predictor variables. As we examined seven frequency bands and included two predictor variables, we now employed a significance criterion of 0.004 (=0.05/[7×2]).

EEG Data
Grand average ERPs for the nogo stimuli in the three blocks for the right occipital site O2 are displayed in Figure 1. Topographies of the P1, N1, and P2 components in the three blocks are also displayed. Grand averages of the results of the wavelet analyses performed on the individual ERPs for the seven frequency bands, which estimate EP on O2 for the three blocks, are presented in Figure 2. Furthermore, the grand average results of the wavelet analyses on the raw EEG, which estimate TP, are displayed in Figure 3.

Issue 1: ERP Components Described as the Sum of Evoked Oscillations in Specific Frequency Bands
The P1, N1, and P2 components reached largest amplitudes in the 80-100 ms, the 120-140 ms, and the 200-220 ms time windows, respectively. Our goal was to assess what frequency bands strongly contribute to the ERP components in this study. Therefore, we restricted our analyses to these three time windows.

Figure 1.
the grand average erPs at the occipital electrode o2 for the nogo stimuli in the happy, Angry, and sad blocks. the topographical maps of the P1, n1, and P2 components clearly display an occipital focus, which justifies the decision to focus on the o2 electrode in our analyses three predictors (θ 1 , α 2 , and a constant; R 2 = .61) and P1 amplitude, F(2, 120) = 93.2, p < .001. The same pattern was observed for the sad nogo stimuli as a significant relation was observed between three predictors (θ 1 , α 2 , and a constant; R 2 = .52) and P1 amplitude, F(2, 120) = 63.9, p < .001. In all cases, EP in the α 2 band had a positive contribution while EP in the θ 1 band and the constant had a dampening effect on P1 amplitude.

thE 80-100 Ms intErval (thE p1 coMponEnt)
The analyses for the Happy block showed a highly significant relation between three predictors (θ 1 , α 2 , and a constant; R 2 = .41) and P1 amplitude, F(2, 120) = 41.4, p < .001. Inspection of the regression coefficients (see Table 1) indicates that EP in the α 2 band had a positive contribution to P1 amplitude, while EP in the θ 1 band and the constant had a dampening effect. Analyses for the angry nogo stimuli revealed a nearly identical pattern. A significant relation was observed between the grand average after logarithmic transformation of individually estimated evoked power (in μv 2 ) at the occipital electrode o2 for the lower theta (θ 1 ) up to the higher beta (β 2 ) bands determined on the basis of the erPs based on nogo stimuli in the happy, Angry, and sad blocks. values along the Y-axis concern a logarithmic scale. the grand average after logarithmic transformation of estimated total power (in μv 2 ) at the occipital electrode o2 for the lower theta (θ 1 ) up to the higher beta (β 2 ) bands determined on the basis of the raw eeg on nogo stimuli in the happy, Angry, and sad blocks. values along the Y-axis concern a logarithmic scale.

thE 120-140 Ms intErval (thE n1 coMponEnt)
The analyses for the happy nogo stimuli showed a highly significant relation between two predictors (θ 2 , and a constant; R 2 = .35) and N1 amplitude, F(1, 121) = 65.2, p < .001. Inspection of the regression coefficients (see Table 1) indicates that EP in the θ 2 band contributed to N1 amplitude, while the constant had a dampening effect. An almost identical pattern (see Table 1) was observed for the angry nogo stimuli (R 2 = .38), F(1, 121) = 74.3, p <.001. For the sad nogo stimuli, the analyses showed a significant relation between three predictors (θ 1 , θ 2 , and a constant; R 2 = .41) and N1 amplitude, F(2, 120) = 41.1, p < .001. Inspection of the regression coefficients indicates that EP in the θ 1 and the θ 2 band contributed to N1 amplitude, while the constant had a dampening effect.

thE 200-220 Ms intErval (thE p2 coMponEnt)
The analyses for the happy nogo stimuli showed a significant positive relation between one predictor (α 1 ; R 2 = .14) and P2

Issue 2: Total Power Decomposed in Evoked, Baseline, and Induced Power
Grand averages of the results of the wavelet analyses performed on the raw EEG for the seven frequency bands, which estimates TP on O2 for the three blocks, are presented in Figure 3. The decomposition of TP in EP, BP, and IP is displayed in Figure 4. Estimated percentages of BP and EP were determined by multiplying the obtained regression coefficients with the observed BP and EP and scaling this by TP. The remaining part to be explained is indicated by the constant, which provides an estimate for IP. Results are reported for each block. We excluded those components (EP, BP and IP) for which the regression coefficients did not satisfy our criterion value (p < .014 for at least two successive time windows). We report only those time windows for which no significant contribution was observed as the majority of the time windows met our criteria.

happy noGo stiMuli
For the θ 1 band, explained variance (R 2 ) by the predictors (IP, EP, BP) for the full time range from 40 to 300 ms was very high (from .71 to .85). On average, the estimated contribution of IP, EP, and BP amounted to 31%, 18% and 51% (see Figure 4). For the θ 2 band, R 2 varied from .74 to .87, and the contributions of IP, EP, and BP were estimated at 32%, 23%, and 45%. For the θ 3 band, R 2 varied from .72 to

Issue 3: The Relation Between Pre-Stimulus Baseline Power and Evoked Power
The goal of these analyses was to determine whether EP in the different frequency bands, which may account for the P1, N1, and P2 components, was strongly related to pre-stimulus baseline activity (BP). As we .10 Note. p < 0.004, ** p < 0.001. Prestimulus baseline power (BP) was used as predictor for the observed evoked power (EP) within a specific time window that corresponds either with the P1, the N1, or the P2 component. Regression coefficients for each frequency band are indicated with d i . We also determined the possible contribution of a constant, indicated with CP. The total amount of explained variance by the analysis is indicated with R 2 . All power values were log10 transformed before performing the analyses. Standard errors (SE) are indicated between brackets.
were interested in the time intervals where the P1, N1, and P2 showed their maxima, we restricted our analyses to the 80-100 ms, the 120-140 ms, and the 200-220 ms time windows.

thE 80-100 Ms intErval (thE p1 coMponEnt)
For the happy nogo stimuli, BP in the α 2 , β 1 , and β 2 bands was a positive predictor of EP in the respective frequency bands (see Table   2). Most relevant seems BP in the α 2 band as this significantly predicted the P1 component. Thus, these data seem in line with the Phase Reset model. However, we also observed that CP in the θ 3 , α 1 , and α 2 band was a significant predictor, which indicates that individual differences in these frequency bands have an additional source, favoring the Evoked model. For the angry nogo stimuli (see Table 3), BP proved to be a significant predictor of EP for the θ 3 up to the β 1 band, but we also observed that CP in both α bands was a positive predictor. For the sad nogo stimuli, BP proved to be a significant predictor of EP for the θ 3 up to the β 2 band, but CP in the α 1 band was also a positive predictor.
Together, these findings seem to support both the Phase Reset and the Evoked model. Importantly, however, explained variance remains quite low, indicating that BP and CP are no strong predictors of EP.

thE 120-140 Ms intErval (thE n1 coMponEnt)
For the happy nogo stimuli, significant BP predictors for EP were found in the α 2 and both β bands but not in the most relevant θ 2 band (see Table 1). The contribution of CP was significant in the θ 3 and both α bands. For the angry nogo stimuli, significant BP predictors were found in the θ 3 up to the β 2 bands, but here we also observed significant contributions of CP in both α bands. For the sad nogo stimuli, we observed significant BP predictors from the α 1 up to the β 2 band, and we observed significant contributions of CP in both α bands. Again, these findings seem to provide some support for the Phase Reset but also for the Evoked model. However, BP in the θ 2 band was not identified as a relevant predictor, even though it was shown to be the main predictor of the N1 component, and the explained variance remains low.

thE 200-220 Ms intErval (thE p2 coMponEnt)
Significant BP predictors for EP for the happy nogo stimuli were present in both β bands. However, we also observed that CP in the α 1 band was a significant positive predictor, which is the band that seems most relevant for the P2 component (see Table 1). For the angry nogo stimuli, significant BP predictors were found in the θ 3 and both β bands. CP in the α 1 band was again a significant positive predictor.
Finally, for the sad nogo stimuli significant positive BP predictors were present in the θ 3 up to the β 2 band, while CP in the α 1 band was a significant positive predictor. In most cases, explained variance remains low. The major exception here is CP in the β 2 band, which in all conditions was a negative predictor for EP. At the same time BP in the β 2 band was a positive predictor. Inspection of Figures 2 and 4 reveals that EP in this time window is absent (the regression coefficients for EP were also non-significant or just significant). Therefore, a relation of EP with BP and CP seems not very meaningful. As BP has a strong positive value, CP will simply be estimated to be negative to end up with a value around zero. .18 Note. p < 0.004, ** p < 0.001. Prestimulus baseline power (BP) was used as predictor for the observed evoked power (EP) within a specific time window that corresponds either with the P1, the N1, or the P2 component. Regression coefficients for each frequency band are indicated with d i . We also determined the possible contribution of a constant, indicated with CP. The total amount of explained variance by the analysis is indicated with R 2 . All power values were log 10 transformed before performing the analyses. Standard errors (SE) are indicated between brackets.

dIscussIon
Three issues were raised in our Introduction that will be addressed by considering the outcome of three different multiple regression analyses. The first issue concerns the extent to which ERP components can be described as the sum of transient evoked oscillations in different frequency bands. The second issue deals with the extent to which overall EEG activity in a specific frequency band (TP) after presenting a visual stimulus (i.e., here facial stimuli that require no response) can be ascribed to stimulus-locked activity (EP), stimulus-induced but not time-locked activity (IP), and pre-stimulus baseline activity (BP). The third issue concerns the extent to which stimulus-locked activity (EP) is due to pre-stimulus baseline activity (BP).

ERP Components Described as the Sum of Evoked Oscillations in Specific Frequency Bands
We focused on three successive ERP components (P1, N1, and P2) that all had a clear occipital focus. With regard to the P1 component, the results of the three different blocks (see Table 1) clearly revealed that its amplitude is strongly positively related to EP in the α 2 band, while a negative relation was observed with EP in the θ 1 band. Additionally, we observed significant contributions of a constant in all blocks. This also concerned a negative relation with P1 amplitude, and might imply contribution of the lower δ band. Thus, it seems that activity in the θ (and possibly δ) band(s) has a dampening effect on P1 amplitude while activity in the α 2 band boosts the P1 component. The relation between α power and the P1 component might underlie the same functionality (see Klimesch, 2011;Klimesch et al., 2004). As activity in the α band is generally interpreted as inhibition, one might argue that the P1 component also reflects inhibition (i.e., the P1 inhibition timing hypothesis proposed by Klimesch, 2011). Such a view implies that the interpretation of earlier results like the enhancement of the P1 component due to visual attention (e.g., see Van der Lubbe & Woestenburg, 1997) requires an update, as this effect is unlikely to reflect gain modulation. However, one could argue that a transient α oscillation like the P1 component is not necessarily related to more tonic oscillations in the α band (see Mishra, Martínez, Schroeder, & Hillyard, 2012). Nevertheless, several studies (see also below) indicate that evoked α power is related to prestimulus baseline α power (e.g., see Fellinger et al., 2011;Gruber et al., 2014;Himmelstoss et al., 2015; see also below).
The results of our analyses for the N1 time window revealed quite consistent results in all three blocks (see Table 1). Namely, the N1 component showed strong negative relations with EP in the θ 2 and also once the θ 1 band. At the same time, positive relations were observed with the constants in the different blocks. These findings suggest that N1 amplitude is boosted by EP in the θ band (see also Klimesch et al., 2004), while it is also dampened by power in the δ band. Although frontal θ has been related to focal attention (Onton, Delorme, & Makeig, 2005), more widespread and also posterior θ is generally linked with drowsiness and deactivation. Therefore, an interpretation of the posterior N1 component as the reflection of a stimulus discrimination process (Vogel & Luck, 2000) may also become a point of discussion (see also Van der Lubbe, Vogel, & Postma, 2005). Again, a transient θ oscillation cannot directly be equated with more tonic oscillations in the θ band, although a clear relation between evoked θ power and pre-stimulus .30 Note. p < 0.004, ** p < 0.001. Prestimulus baseline power (BP) was used as predictor for the observed evoked power (EP) within a specific time window that corresponds either with the P1, the N1, or the P2 component. Regression coefficients for each frequency band are indicated with d i . We also determined the possible contribution of a constant, indicated with CP. The total amount of explained variance by the analysis is indicated with R 2 . All power values were log10 transformed before performing the analyses. Standard errors (SE) are indicated between brackets.
baseline θ power (but see below) would support a common underlying functionality.
Our observations regarding the P2 time window revealed a slightly less consistent pattern (see Table 1). For two blocks, P2 amplitude had a strong positive relation with EP in the α 1 band, while in the Angry block, there was a positive relation with EP in the θ 3 band. These different results might point to subtle differences between this block and the other blocks. Most importantly, the results again show that effects mainly concern frequency bands that are related with inhibition or deactivation.
Altogether, the outcome of these analyses suggests that early ERP components can very well be described as reflecting the sum of EP in various frequency bands. Furthermore, the P1 and N1 components seem related to different oscillatory frequencies and do not reflect alpha ringing. Most importantly, the strong relation between different ERP components and specific oscillations may imply that generally accepted interpretations of effects on these components need to be reconsidered.

Total Power Decomposed in Evoked, Baseline, and Induced Power
Several authors argued that it may very well be the case that most stimulus-related activity is not strictly time-locked to stimulus onset, which implies that focusing on ERPs may be too limited as a major part of relevant activity is averaged out (Buszáki, 2006;Makeig et al., 2004). The current analyses allow us to determine the validity of this idea, by assessing the separate contributions of IP, EP, and BP to TP.
Estimated contributions from 40 to 300 ms after stimulus onset for the different frequency bands and three blocks are displayed in Figure   4. The patterns observed in the different blocks are quite comparable, though not identical.
For the θ 1 band the estimated contributions of IP, EP, and BP, averaged across blocks and all time windows amounted to 31%, 19%, 49%.
Obviously, the contribution of EP is small, while the contribution of BP is remarkably high. Importantly, IP clearly adds to TP, which implies that a major part of stimulus-related but not phase-locked activity is removed after performing the averaging procedure. For the θ 2 band, the contributions of IP, EP, and BP are estimated at 31%, 24%, 44%, and for the θ 3 band, the contributions of IP, EP, and BP are estimated at 27%, 28%, 44%. Thus, the pattern in the different θ bands is more or less the same.
For the α 1 band the estimated contributions of IP, EP, and BP, averaged across blocks and all time windows amounted to 38%, 26%, and 36%. For the α 2 band, the contributions of IP, EP, and BP are estimated at 42%, 16%, and 42%. Thus, the contribution of IP for the α bands is even higher than for the θ bands, while the contribution of EP becomes smaller. Furthermore, the contribution of BP remains strong.
Inspection of Figure 4 also reveals that in general the contribution of IP to TP increases over time, while the contribution of EP decreases.
For the β 1 band, the estimated contributions of IP, EP, and BP amounted to 25%, 8%, and 67%, and for the β 2 band, the estimated contributions were 6%, 2%, and 92%. Here strong reductions were observed for IP and especially for EP, while TP seems largely due to BP (see Figure 4).
Together, our results support the aforementioned idea that focusing solely on ERPs, thus evoked activity, ignores a major part of stimulusrelated activity. This especially concerns activity in the θ and α bands, while activity in the β 2 appears not stimulus-related. The latter observation does not exclude the possibility that this frequency band plays another role by transmitting information by phase changes, but apparently these phase changes are not related to stimulus onset, otherwise they should have become visible in EP. A more general observation is the strong presence of BP for all frequency bands. This suggests that a major part of EEG activity after stimulus onset is not phase reset by this stimulus. Furthermore, the major presence of induced activity in most frequency bands also indicates that activity that is not phase-locked cannot be considered as irrelevant background activity. The latter two observations seem quite relevant for the discussion of our third issue.

The Relation Between Pre-Stimulus Baseline Power and Evoked Power
Are ERPs indeed due to a phase-reset of ongoing oscillations, as was proposed by Başar (1999) Table 3), BP in the α 2 band predicts EP (54%), while CP again has a strong contribution (46%). Finally, in the Sad block (see Table 4), BP predicts EP (64%), while CP has a clear con- faces the same problem as non-evoked activity is considered to be background activity. In the following section we will examine whether some recently proposed models may provide a better explanation for our data than the Evoked and the Phase Reset model.

Alternative Models Accounting for the Role of Pre-Stimulus Baseline Power on Evoked Activity
Our focus was restricted to early ERP components and we concluded that the Phase Reset model provides only a minor contribution to EP.
Other studies clarified that the Phase Reset model cannot account for later (often denoted as endogenous) ERP components (e.g., see Barry, 2009). However, the Evoked model seemed also insufficient. Thus, the relation between pre-stimulus baseline activity and early ERP components appears to be more intricate than a simple phase reset. In the last decade, several studies revealed that spatial attention modulates baseline activity in especially the α band (e.g., see Thut, Nietzel, Brandt, & Pascual-Leone, 2006;Van der Lubbe & Utzerath, 2013;Worden, Foxe, Wang, & Simpson, 2000). The general observation is that when attention is directed at one side of the visual field, α power is larger at ipsilateral than at contralateral occipital sites, and this increased ipsilateral α power is thought to reflect inhibition. Recent ideas became even more specific (Jensen & Mazaheri, 2010;Mathewson, Gratton, Fabiani, Beck, & Ro, 2009;Mazaheri & Jensen, 2008;Schalk, 2015).
Schalk (2015) proposed the function-through-biased-oscillations (FBO) hypothesis, which states that oscillatory voltage rather than oscillatory power reflects cortical excitability. This may show up in more efficient behavior and increased amplitudes of early ERP components (see Mathewson et al., 2009). In the case of strong oscillations in the α band, there are transient phases of facilitation and inhibition, which depend on the phase (peak or trough) of the oscillation, while in the case of weak oscillations, there is a more tonic phase of facilitation. This view implies a more indirect relation between pre-stimulus baseline activity and evoked (but also induced power), which may explain the low amount of explained variance of EP. Furthermore, this hypothesis also implies cross-frequency coupling between BP and EP as a reduction in α oscillations may release a slow oscillation like the contingent negative variation (CNV). An appropriate test of this model seems to require the analysis and selection of single trials, which is beyond the scope of the current approach. Klimesch et al. (2007) presented an alternative idea. They proposed the Event-Related Phase Reorganization (the ERPR) model, which implies that only those oscillations that are task relevant will be reset, while other oscillations remain unaffected. This idea may explain why in our analyses only weak support was obtained for a phase reset, as we focused only on the NoGo stimuli that required no response, although they were intermixed with Go stimuli. A proper test of this model might be a comparison of different tasks with identical stimuli, requiring either simple stimulus detection or stimulus discrimination.

Some Caveats of the Chosen Analyses
The choice of certain parameter settings in our analyses may have some limitations. First, we employed a log10 transformation of the individually obtained power values (in μV 2 ). This approach was chosen to reduce major individual differences. However, a disadvantage of this transformation is that the observed relation between the different variables is not so easy to interpret. Another, probably more insightful approach is to perform the analyses with non-squared amplitudes 1 and leave out the transformation. Secondly, the chosen value of the c parameter for the wavelet analyses (5) implies that the temporal resolution is not the highest. This results in a smoothing of the estimated power, which is well visible in Figure 2, as the evoked power in the α and θ bands starts before stimulus onset. Nevertheless, as a logarithmic scale was employed this effect looks worse than it really is. We determined BP in the 500-200 ms window, which implies that for most of our results this filtering artefact played no role. Nevertheless, it may have some influence for the θ 1 and θ 2 bands. An implication may be that the contribution of BP to TP is overestimated for these sub-bands.
Furthermore, it might explain part of the correlation between BP and EP in these frequency bands. However, inspection of Tables 2 to 4 shows no such effect, which indicates that the chosen parameter value induced no major problem. The advantage of a low temporal resolution is a better frequency resolution, which also implies that individual differences in peak latency of EP will play no major role. Nevertheless, one might consider the possibility to lower the c parameter to 3, which will improve the temporal resolution.

conclusIons
In conclusion, the P1, N1, and P2 components can by and large be described as transient oscillations in the α and θ bands. The contribution of IP to TP is mostly larger than of EP, which confirms that focusing