Amplifiers, sampling and recording

Why this matters

Between the scalp and your first plot sits an amplifier, an analog-to-digital converter, a set of hardware filters, a clock, and a file format, each of which has already made decisions about your data. The sampling rate in the header does not tell you the usable bandwidth; the trigger channel does not tell you when the stimulus appeared; the file’s timestamps do not guarantee that no samples were lost. Every one of these is a documented failure mode in real public datasets. This lesson teaches you to read what the acquisition system recorded about itself, and to check it.

Concepts

Differential amplification and common-mode rejection

An EEG amplifier does not measure the potential at an electrode; it measures the difference between two inputs, electrode and reference, and amplifies that. Any signal that is identical at both inputs, the common-mode signal, is subtracted away. Mains interference coupled onto the whole body is the classic common-mode signal, and the microvolt brain signal is the differential one. How well an amplifier removes the common-mode part is its common-mode rejection ratio (CMRR), quoted in decibels (TODO(confirm) typical values the author wants quoted for research amplifiers).

Rejection is only as good as the balance of the two inputs. If the two electrodes have very different impedances, the common-mode signal reaches the amplifier with different amplitudes at the two inputs, so part of it no longer cancels and appears as line noise in that channel. That is the practical reason impedance is checked (L0.2). The ground electrode gives the amplifier its zero for this subtraction; without it the common-mode voltage can exceed the amplifier’s input range.

DC versus AC coupling, and the hardware high-pass

The electrode–skin interface produces slowly varying offsets of many millivolts, thousands of times larger than the EEG. An AC-coupled amplifier removes them with a hardware high-pass filter (a cutoff on the order of 0.1 Hz or higher) before digitization; a DC-coupled amplifier digitizes from 0 Hz with a large enough input range to hold the offset. The choice is written into the data forever: an AC-coupled recording has already lost its slowest content, and a DC recording carries drift you will have to handle yourself. The curriculum’s datasets span both: ds-eegbci was recorded with no hardware filters at all; ds-iowapd carries a 0.1 Hz online high-pass; ds-lemon’s raw release is band-limited to 0.015–1000 Hz; ds-dortmund has a 250 Hz online low-pass and no online high-pass. Read the header, then read the dataset description, because headers do not always know.

Bit depth and microvolts per least-significant bit

The analog-to-digital converter turns a voltage into an integer. Its resolution is the input range divided by the number of levels: for a range of ±V volts and b bits, one least-significant bit (LSB) is 2V / 2^b. A ±5 mV range at 16 bits gives about 0.15 µV per LSB; the same range at 24 bits gives about 0.0006 µV per LSB (these are arithmetic illustrations, not device specifications). Sixteen bits is enough for an AC-coupled system whose offsets have been removed; DC systems with large input ranges rely on 24-bit converters so that the microvolt signal is still resolved on top of the millivolt offset. File formats carry this scaling: EDF stores 16-bit integers with a physical-minimum/maximum calibration in the header, BDF stores 24-bit integers, and a wrong calibration field makes every trace wrong by a constant factor.

Anti-alias filtering, and why bandwidth is not Nyquist

Sampling at rate fs can represent frequencies only up to fs/2, the Nyquist frequency; anything above it does not disappear but aliases, reappearing at a lower frequency indistinguishable from real content. So every acquisition system low-pass filters the analog signal before digitizing it. That hardware anti-alias filter is usually set well below Nyquist, and consumer systems often decimate from a high internal rate after a low-pass that ends far below the output rate. The consequence is a rule you will use for the rest of the curriculum: the sampling rate does not tell you the usable bandwidth. ds-arithmetic is sampled at 500 Hz but its descriptor reports a “30 Hz cut-off”; the consumer-headset datasets in the directory output 128 or 256 Hz samples from hardware whose bandwidth is about 43 Hz and which includes built-in mains notches (§10.9). Level 1 makes aliasing quantitative; the pitfall entry on hardware bandwidth is the one to remember here.

Line-noise pickup

Mains interference at 50 Hz or 60 Hz (by country; ds-brainlat mixes both within one dataset) reaches the recording by capacitive coupling from cables and the environment, through ground loops, and through any imbalance that defeats common-mode rejection. It shows as a sharp spectral line plus harmonics. Some systems remove it with a hardware notch before the data are stored, leaving a hole in the spectrum (ds-arithmetic at 50 Hz, ds-mouse at 60 Hz, the consumer sets); others leave it in (ds-eegbci, ds-lemon, ds-respect, ds-pearl-neuro). Both are facts to read from the description before L1.6 tells you how to remove what is left.

Events, triggers, annotations and clock synchronization

An event is a time-stamped label. It reaches the file in one of three ways:

• Hardware triggers: a digital code (a TTL pulse or a bit pattern) sent by the stimulus computer into a dedicated trigger input of the amplifier and sampled with the same clock as the EEG. This is the most precise route, because the trigger and the data share one clock.
• Software markers: events written by the acquisition software from messages it received, timestamped with the acquisition computer’s clock.
• Annotations: labelled time spans (onset, duration, description) added during or after recording: bad segments, block boundaries, eyes-closed periods. MNE represents both events and annotations; annotations carry durations, events do not.

Two timing errors follow from this architecture, and both have pitfall entries. Trigger latency: the trigger marks when the computer sent the stimulus, not when the screen displayed it or the sound reached the ear; monitor refresh, graphics buffering and audio latency add a delay that is usually constant within a setup but differs between labs. The only measurement that settles it is a photodiode on the screen (or a microphone at the speaker) recorded as an extra channel, whose onset can be compared with the trigger directly. Dropped samples and clock drift: when the stimulus stream and the EEG stream are timestamped by different clocks, or when the acquisition buffer overflows, samples are lost or the two clocks diverge, and events drift relative to the data across the recording. Multi-stream systems (LSL and its XDF file format) address this by recording every stream’s clock offsets so that streams can be aligned afterwards, provided nothing was dropped.

File formats you will meet

Whatever the format, the loader produces the same object, and its info is where you read the acquisition metadata: sfreq (sampling rate), highpass and lowpass (the hardware filter settings the file claims), nchan and channel types, bads, and meas_date. Treat every one of those values as a claim to be checked, not a fact: the header’s high-pass and low-pass fields are frequently defaults written by the converter rather than the amplifier’s settings, and L0.6 shows a file whose header sampling rate is simply wrong.

The data behind this lesson

• The notebook loads each spine dataset in its native format: ds-eegbci (EDF+), ds-lemon raw (BrainVision) and ds-erpcore (format and access TODO(confirm), §13 item 22; if it cannot be fetched, ds-brain-invaders stands in). ds-iowapd (EEGLAB) supplies a fourth format.
• The trigger-offset exercise needs a recording with a photodiode channel. No spine or directory dataset documents one (TODO(confirm) — §6 L0.3), so the exercise uses a synthetic recording with a known stimulus–trigger offset, generated by the notebook or by data/scripts/ (a synthetic file carries synthetic: true, derived_from and a modifications list in its sidecar, §4.5). The exercise says so; the answer key comes from the notebook. The trigger-offset pitfall’s figure shows such a recording with a planted 23 ms offset; the exercise’s own value need not be the same.

Explore

Set a signal with one component well above half the sampling rate and watch its samples trace out a slower wave; switch the anti-alias filter on and watch that component vanish before sampling rather than fold. Then lower the sampling rate until a component you care about is lost, and note that the reconstruction from the samples matches the continuous signal only while the sampling theorem holds. The spectrum before and after sampling makes the folding explicit; L1.1 gives the arithmetic.

Practice

The notebook loads one file from each spine dataset in its native format, prints info, lists channel types, counts events per code, checks for timing gaps between the first and last sample, and loads the synthetic photodiode recording whose stimulus–trigger offset the exercise asks for.

Exercises