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So my 30,000 ft. understanding of the EEG signal processing data flow is:

  1. Capture raw EEG data ("raw waveforms")
  2. Run these raw waveforms through a Signal Processing Framework that consists of 1+ "nodes"/processors, where each processor is doing some kind of transform on the raw waveform. In doing so, new information is unlocked from the raw waveform that was previously hidden
  3. Perform individual analyses on this unlocked data based on what suits your research/application

So first off, if the above understanding is misled in any way, please begin by correcting me!

Assuming I'm more or less correct, my specific application at hand is that I want to correlate certain raw waveforms with events (such as "thinking of a turtle", "moving head up and down", etc.). I believe Event-Related Potentials are what I'm looking for, but...

What I'm struggling with is: what does my "Signal Processing Network" need to look like in order to implement ERP? From an architectural perspective, I'm looking for this "network" to take raw waveforms in as input, and to output events, like the few I mentioned above.

Is FFT a player here? Some kinds of filters? What processors comprise an ERP system, and what does their respective "network" (data flow pipeline) look like?

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    $\begingroup$ Thanks @daniel - when you say "of course the data will be transformed from the time to frequency domain", why do you say "of course"? What is there to be gained by viewing the data in the frequency domain over viewing it in the time domain? $\endgroup$ – smeeb Apr 9 '16 at 8:07
  • $\begingroup$ In particular the goal is often to get an idea of the distinct frequencies that comprise a complex signal, and if the signal is really complex it may be impossible get that information by observing the time signal. $\endgroup$ – daniel Apr 9 '16 at 15:54
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    $\begingroup$ Thanks @daniel - let's stick with your heart rate example. You stated "You are typically looking for the average behavior of a signal over time." Can you provide 1 concrete example of one such "behavior" about the human heart that can be observed by running heart rate data (observed in the time domain) through FFT and transforming it into the frequency domain? $\endgroup$ – smeeb Apr 9 '16 at 16:00
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    $\begingroup$ Sure, so can you provide any concrete example where decomposing an original waveform into component frequency-based waveforms yields more actionable information than on the original waveform? Any example at all, but a concrete example? $\endgroup$ – smeeb Apr 9 '16 at 16:33
  • $\begingroup$ Thanks again @daniel, but I'm just not seeing the value of this (still). Let's use your violin example. If we already know what the violin sounds like, why break it down into its major frequency components? To reconstruct the sound of the violin?!? We had the sound in the first place! To me, this is like saying: let's tear a car engine apart so we can have all its individual parts...so we can then put the car engine back together...and have ourselves a car engine! No, you already had the car engine in the first place! $\endgroup$ – smeeb Apr 9 '16 at 18:19
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Event-related potentials are an issue in many aspects of physiology, not just in EEG analysis, so this answer is more general.

The main problem is that electrical or other signals that are associated with some "event" are typically much lower in magnitude than the background noise in the system being examined. Electrocardiograms are the exception in this regard. The trick then is to get the event-related signal out of the noise.

This is done by multiple repetitions of the "event" combined with signal averaging. You mark the electrical record with the time of each event, line up portions of the record by the event markers, and average the lined-up signals around the multiple events. This can be the full waveform for sensory evoked potentials, or if you are examining action potentials in a nerve, the histogram of post-event occurrence times of action potentials.

The particular signal-processing mechanisms used have evolved with technology. I'm old enough to have known people who 60 years ago recorded electric neural activity on magnetic tape and processed the data, after analog-to-digital conversion, on what were then state-of-the art computers with 65,000 words of memory. Even then, there was discussion about the best technologies to use for specific purposes, as this 1959 MIT monograph indicates.

The main problem, the low level of event-related signals to the noise from other electrical activity, still remains 60 years later. The noise is biologic rather than technical, so more recent improvements have more to do with ease and speed of processing rather than the fundamental signal-to-noise problem. For event-related potentials, use whatever technology allows you to collect the electrical data along with linked notations of the event times, then to average the signals synchronized on the events to build up the signal out of the noise. In a standard clinical application of brainstem auditory evoked potentials to evaluate hearing, you may need to average over 500 or more stimulus presentations.

This signal-in-noise problem is also seen in functional magnetic resonance imaging (fMRI) of brain function, which must consider not only the signal over time but also differences among brain regions within individuals and differences among individuals. The Wikipedia page on fMRI goes into some detail on methods for getting specific signals out of the background noise. You should pay particular attention to the issue of "Block versus event-related design" on that page. My understanding is that for "events" of the type that you consider, like "thinking about a turtle," the block design works best in fMRI. The paper by Thierry et al, provided in the helpful answer by @Christiaan, shows how to apply this type of blocking approach to EEG measurements during presentation of visual stimuli.

The methods in that paper by Thierry et al also indicate the type of practical care that is used in professional analyses of this sort. The authors go into detail about the nature and placement of the electrodes, choice of which electrodes to use for analysis, signal-sampling rates, and so on. For example:

Scalp activity was digitized at a 1-kHz sampling rate from 64 Ag/AgCl electrodes distributed throughout the scalp according to the 10–20 convention using Cz as a reference. Impedances were kept below 7 kOhms. The electroencephalogram was filtered on-line between 0.01 and 200 Hz and off-line low pass at 35 Hz using a zero phase-shift digital filter. Eye blink artifacts were mathematically corrected, and signals exceeding $\pm$ 75 $\mu$V in any given epoch were automatically discarded.

Reading papers like this are probably the best way to learn about what's involved and to find people who can teach you how to do it.

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    $\begingroup$ This seems like a reasonable answer to me. Does filtering play a role in this? $\endgroup$ – daniel Apr 9 '16 at 17:09
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    $\begingroup$ @daniel, filtering is inherent in all this signal processing as any real recording system has finite bandwidth, and that bandwidth must include the signal of interest. In this type of application the electrical recording is typically AC-coupled so that low-frequency signals (e.g., drift) are omitted. If the particular waveform of the response is known then filtering to emphasize its frequency components could help, but the main technique is multiple repetitions of the event and averaging the multiple signals after they have been lined up by event times. $\endgroup$ – EdM Apr 9 '16 at 17:22
  • $\begingroup$ Thanks for the great answer @EdM (I'd upvote it if I had the rep to do so)! So it sounds like the two main problems with "raw" EEG data are: (1) signal-to-noise ratio (which is a long-standing problem seeing that the majority of the noise is coming from the subject's own body) and (2) using tricks like FFT (as well as others) to unlock more information than what was present in the original waveform. Can you please confirm these statements and correct me if I am misunderstanding or overlooking anything? Thanks again! $\endgroup$ – smeeb Apr 9 '16 at 18:29
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    $\begingroup$ FFTs don't "unlock more information than what was present in the original waveform," they just help to bring a signal out of the noise in some circumstances. That's really an important distinction; the information is there but you have to find it. Yes, signal-to-noise is the main issue. For your application, signal averaging in the time domain may be more important than frequency-domain analysis with FFT, unless you happen to know the frequency characteristics of the signal you are looking for. $\endgroup$ – EdM Apr 9 '16 at 18:36
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    $\begingroup$ @Masi : ECG signals are typically very large with minimal noise when electrodes are properly applied and high-quality electronics are used; don't know that there's much "physiological" noise to find within them. The more general case is beyond my current professional expertise, as I haven't had to think about signal processing in many years. I recall that wavelet analysis can be useful for finding signals of a specified shape in a noisy signal, in a way that's superior to Fourier analysis, but I have no direct experience with that. $\endgroup$ – EdM May 18 '16 at 16:24
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ERPs are typically analyzed in terms of amplitude and latency. FFT is not really an option; it doesn't make sense. There may be some applications where it may be useful, but these are quite specific. For example, if repeated stimuli are presented and you are not averaging them, but you are collection an EEG, then FFT may help you to deduce whether stimulus frequency (e.g. 1/s) matches the response frequency and what the phase difference is between them. Note that FFT yields amplitude and phase data. But generally, again, ERPs are analyzed simply by taking amplitude and latency (Fig. 1)

ERP analysis
Fig. 1. ERPs are characterized by taking the peaks, here the positive peak (P) at 100 ms (P1) and the negative peak (N) at 170 ms (N170). The amplitude of the N170 peak was analyzed and plotted. source: Thierry et al., (2007)

Reference
- Thierry et al., Nature Neuroscience (2007); 10: 505-11

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    $\begingroup$ As always, thanks again @Christiaan! Please see my last comment/followup question underneath EdM's answer...I have the same question for you! Thank you immensely! $\endgroup$ – smeeb Apr 9 '16 at 20:39
  • $\begingroup$ @smeeb - Filtering is only necessary when it's necessary. If it's not, it's not :) $\endgroup$ – AliceD Apr 9 '16 at 22:28
  • $\begingroup$ ...Fast Fourier transform (FFT) of EEG data, is ...a reformatting of data into component frequencies. This transformation is useful because many pathological EEG patterns produce spectral patterns that can be easily recognized without the extensive training required to interpret routine EEG tracings... From the abstract of this paper. Clearly FFT does make sense and is done in some cases. $\endgroup$ – daniel Apr 10 '16 at 2:48
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    $\begingroup$ QEEG [FFT/wavelet analysis] has been accepted for clinical application in some areas, such as cerebro-vascular disorders and epilepsy, though it remains yet to be accepted in other clinical areas, such as diagnosing mild traumatic brain injury or psychiatric disorders. en.wikipedia.org/wiki/Quantitative_electroencephalography. $\endgroup$ – daniel Apr 10 '16 at 3:15
  • $\begingroup$ @daniel - that's EEG, not ERP; question & answer are on ERP $\endgroup$ – AliceD Apr 10 '16 at 5:24

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