How to decide on the right EEG spectral analysis method in BrainVision Analyzer

To find out the answer to this question, it is necessary to ask yourself: Do I only want to look at the frequency of the signal or do I also need the time information simultaneously?

FFT would be the best option since it transforms time-domain EEG data into frequency domain. It tells you how much of a frequency is contained in the total period of observation. This means that the outcome of FFT, which is termed spectrum, has no time but only frequency information. Commonly, FFT is performed on data collected in blocked designs. For instance, the aim would be to compare the induced frequency modulation in resting blocks versus active blocks, task A versus task B or before versus after medication. Usually, data is split into short epochs or segments, each segment goes through frequency decomposition, and the obtained frequencies for all segments per condition are averaged together to get an idea of the frequency activity within the blocks. Through averaging the spectra, the non-task related variability will be eliminated and gives a better signal-to-noise-ratio.

The so-called time-frequency analysis methods would be the right choice. In Analyzer, you have three transformations to select from – Wavelets, ERS/ERD and Complex Demodulation. In principle, they serve the same purpose which is enabling you to investigate the spectral dynamics of a signal across time. They are commonly applied in event-related designs in the same way as ERPs.

If time-frequency analysis is your final goal, to further narrow down the method selection, the next question to be answered is: Do I already have an idea which frequency range to investigate, or do I rather want to explore a wider range of frequencies?

ERS/ERD as well as Complex Demodulation are suitable methods for investigating the spectral dynamics of EEG data across time within a specific frequency band (i.e., narrow band). Thus, a priori information regarding the frequency band of interest is required. With this information, the common approach is to isolate the EEG data to a desired frequency band (e.g., the alpha band) by filtering, prior to applying ERS/ERD or Complex Demodulation.

On the other hand, Wavelets are used in a situation where you want to examine the spectral dynamics across multiple frequency bands. Depending on the sampling rate (Fs) used during data recording, it is possible to generate a time-frequency plot (commonly represented as a heatmap) that covers activities from 0 Hz up to Nyquist frequency (i.e., half of the sampling rate).

Figure 1 illustrates a decision tree that helps in identifying the optimal spectral analysis method.

Having decided on the spectral analysis method, you are just one step away from generating the results by using the transformations implemented in Analyzer. All of them can be found in the Frequency and Component Analysis group under the Transformations tab of the ribbon menu. Nevertheless, to ensure that the analysis is performed correctly, some factors should be taken into consideration so that the analysis results are interpretable.

The length of the data segment plays an important role when conducting spectral analysis. This is because with an improper segment length, the outcome of the spectral analysis could be jeopardized. Therefore, it is worthwhile to think of this before the analysis. In some cases, one might already need to adjust parameters when designing the experimental paradigm. Essentially, spectral analysis is mostly performed on segmented data or shorter segments instead of long continuous data.

FFT

One crucial assumption for FFT is that the data should be stationary or at least quasi-stationary, in the sense that the spectral properties vary slowly with respect to the main frequency. Depending on which frequencies you’re interested in, in theory the segment should be long enough to include at least one cycle of the lowest frequency of interest. To give an example, if 8 Hz is the lowest frequency of interest, the segment length should be at least 125 milliseconds (i.e., Period =1/frequency) long. But practically, it is recommended to have several cycles of the signal to ensure full frequency information can be extracted. Lower frequency means longer data segment. In sum, segment lengths of one or two seconds are suitable for studying frequencies from delta to beta or higher. Meanwhile, please keep in mind that longer segments should be avoided as the signal might become non-stationary.

Wavelets

Like in FFT, segment length should be adapted to cover several cycles of the lowest frequency of interest. Thus you may choose a different length as for ERP. In particular, if you consider normalizing the wavelet result, it is recommended to include safety margins at the beginning and end of the reference interval as well as the post-stimulus interval.

The safety margin is half of the Wavelet length, which is mathematically expressed as c/(2*min(f)). c is the Morlet Parameter, indicating number of Wavelet cycles and min(f) represents the lowest frequency of interest [1]. As an example, by fixing the Morlet Parameter to five, and the lowest frequency to be investigated is in the theta frequency band, the safety margin should be at least 625 milliseconds (i.e., 5/(2*4 Hz)). This calculated value needs to be considered in determining the segment length.

ERS/ERD and Complex Demodulation

In general, the segment length should be long enough to avoid transient effects at both segment borders due to filtering. As mentioned, the input data for ERS/ERD and Complex Demodulation are required to be narrow-band and band-pass filtering is normally applied to achieve this. In Complex Demodulation another low-pass filter is applied to the down-modulated data [2].

For a fixed sampling rate, frequency resolution is entirely determined by the number of data points or segment length. Longer segments will have a higher frequency resolution. This means the frequency bands can be divided into more frequency bins, allowing for a finer distinction within bands. The frequency resolution is defined as the ratio of sampling rate to number of data samples in a segment (i.e., Fs/N). For example, for a dataset sampled with 512 Hz and a segment length of one second, the maximum frequency resolution is 1 Hz (i.e., 512/512), while segments of two seconds allow for 0.5 Hz (512/1024). In Analyzer, the maximum resolution will be internally calculated and displayed when applying FFT.

The Morlet Parameter (c) plays an important role in adjusting the trade-off between time and frequency resolution. It indicates the duration of each Wavelet and the spectral bandwidth that is captured with it. A smaller c implies fewer cycles, thus shorter Wavelets, lower frequency resolution and a higher temporal resolution; a larger c implies more cycles, thus longer Wavelets, higher frequency resolution and a lower temporal resolution. Wavelets with five cycles provide a good trade-off between time and frequency resolution, therefore it is commonly used in various EEG analyses [3].

Regarding the range and number of frequency steps, there are no standard guidelines. The maximum frequency is restricted either to Nyquist frequency or to below the cutoff of a low-pass filter. Effectively, it should be defined depending on the frequencies of interest, e.g., 1 – 40 Hz. Meanwhile, the number of frequencies steps (i.e., Wavelet layers) should be set to achieve the desired width of frequency bands, e.g., 40 frequency steps.

If you’re interested in studying the effects across frequency layers, we often advise to use the option logarithmic steps due to the consistent overlap of the wavelets. Nevertheless, the linear scale can be used if you need to extract a layer at a precise frequency or if you want to interpret each frequency layer separately.

Sometimes you might want to express the spectral analysis result on a different scale for comparison purposes. That is where normalization comes into play. Let’s take a look at the normalization options available in Analyzer for each spectral analysis method.

FFT

You have the option to specify the frequency range for the normalization factor. The values in each frequency bin of the computed amplitude/power spectrum are expressed as relative values (i.e., expressed in percentage (%)) with respect to the sum within the defined range, as shown in Figure 3. This relative measure facilitates comparisons between subjects or channels, as it eliminates inter-individual differences in absolute amplitude/power. The relation can be calculated with a single band (e.g., to get theta-beta ratio), a broader band or the full spectrum.

Wavelets

Five normalization options are available in the Wavelets transformation – Baseline Correction, Normed Output, Percent Change, Decibel and Z-transform. They are similar to each other with regard to what they are doing, however, what is used as reference value for the normalization is different. You can find detailed descriptions and corresponding mathematical formulations underlying the normalization options in the Analyzer User Manual. The reference interval should be selected so that it covers a time period that does not show pronounced activity and that it avoids overlap with segment borders as well as stimulus onset.

Briefly, Baseline Correction will subtract the mean activity of a reference interval, while Normed Output and Decibel will rescale the data, and Percent Change and Z-transform will do both. Sometimes, it would be sufficient to use the Baseline Correction, as it subtracts background activity that might be task-unspecific and thereby result in a common baseline level across groups/conditions. This could already alleviate variability across Wavelet layers and participants and make experimental groups more comparable.

However, it might be desired to also apply a rescaling to the data, so that any comparisons would not have to be based on absolute values but rather on relative values. This would be beneficial if your experimental groups vary within different amplitude ranges.

Normalization in Analyzer is performed per segment, frequency layer and channel, so called single-trial normalization, which is suitable for clean segments without outliers in the baseline period. Alternatively, normalization can also be performed on the averaged data [4]. If you’re interested in a workaround for this type of normalization, please contact us.

It is recommended to check which normalizations are usually reported in publications if you want to make your results more easily interpretable to peers and comparable to similar studies. This is because there might be different preferences for certain normalizations across research fields or maybe even for certain paradigms.

ERS/ERD

In contrast to FFT and Wavelets, normalization is considered an integral part of the ERS/ERD calculation. There are two options available. You can choose to express the analysis result either in percentage or decibel with respect to a reference value. The mathematical formulations of these options can be found in the Analyzer User Manual. Adhering to the standard definition of ERS/ERD [5], mean power within the reference interval is computed. But median can be used alternatively if there are a lot of outliers in the reference interval. The reference interval should be defined in the same way as in Wavelets. Unlike Wavelets, the normalization in ERS/ERD is performed on the averaged power values.

Complex Demodulation

There is no normalization option incorporated in this transformation, but it is possible to normalize the outcome using the official Percent Change solution that can be downloaded from our website.

There is an additional important feature of the ERS/ERD method which might be worth to know, though it is an optional step. As we often do in ERPs when we extract the amplitude information of a peak or time range, we average across data points. This gives us a more reliable estimate of amplitude values that is not biased that much by fast fluctuations or outliers.

In the ERS/ERD transformation, this is implemented via a moving average. The moving average is performed by first specifying a time window, then each data point of the ERS/ERD result will be replaced by the mean of the specified time window around that data point. Eventually, the ERS/ERD result is smoothed. However, note that there will be some artifacts at the edges of the segment because of missing values outside of the segment borders. This effect disappears after half of the smoothing window.

Increasing the window size improves the smoothing, but at the same time decreases the accuracy. The authors of a review paper [5] recommend using a longer average time across data points if there are very few trials, while a shorter average interval should be sufficient if there is a lot of trials. This is because the effect of both averages (across time and across trials) leads to a similar result. Another study suggests that half a period of the frequency of interest would be an optimal window for averaging, that is 50 milliseconds for studying the alpha band [6].

To recapitulate, FFT is done when oscillatory effects are expected and to get a spectral characterization of a quasi-static brain state. An example use-case would be computing alpha power in a resting-state paradigm. Time-frequency analysis methods are used when effects are expected to be transient in time. They can be used in an event-related paradigm to investigate phase-locked and non-phase locked activities.

The table below summarizes important prerequisites and depicts how the output of each method looks like.