Spectral Analysis

Spectral analysis is where raw EEG becomes clinically readable. The preprocessed time-domain signal—a squiggly line of voltage over time—is decomposed into its frequency components, revealing how much power the brain is producing in each frequency band, where on the scalp that power is concentrated, and how the left and right hemispheres compare. This is the foundation of quantitative EEG.

The Coherence Workstation computes spectral power via Welch’s method, extracts band power across clinical frequency bands, fits the aperiodic (1/f) spectral slope using specparam, and computes hemispheric asymmetry for seven homologous electrode pairs. Each of these steps has parameters that affect the result, and each parameter is documented here.

Welch’s Method

Power spectral density (PSD) is estimated using Welch’s method—a windowed, averaged periodogram that trades frequency resolution for statistical stability. The signal is divided into overlapping segments, each segment is windowed (Hann window), an FFT is computed for each segment, and the resulting power spectra are averaged.

spectral:
  fmin: 0.5
  fmax: 50.0
  n_fft: 1024

Frequency range: 0.5–50.0 Hz. The lower bound matches the high-pass filter cutoff, ensuring the PSD includes the full delta band. The upper bound captures the full gamma band (30–50 Hz) while stopping below the notch filter frequency (60 Hz). This range is wider than what many clinical pipelines compute—some stop at 30 Hz—because the Coherence Workstation includes gamma and high-beta analysis as standard features.

FFT size: 1024 points. At a 256 Hz sampling rate, this gives a frequency resolution of 0.25 Hz (256/1024). This is fine enough to resolve the clinical sub-bands (Alpha1 vs. Alpha2 boundary at 10.5 Hz) without requiring excessively long data segments. Each Welch segment is 4 seconds long (1024/256), which provides a good balance between frequency resolution and temporal stationarity—EEG is approximately stationary over 2–4 second intervals but may drift over longer periods.

Frequency Band Definitions

The pipeline uses clinical-standard frequency band boundaries following the EEGLAB/Thatcher/Kaiser convention:

spectral:
  bands:
    Delta: [1, 4]
    Theta: [4, 8]
    Alpha: [8, 13]
    Alpha1: [8, 10.5]
    Alpha2: [10.5, 13]
    Beta: [13, 30]
    Beta1: [13, 15]
    Beta2: [15, 18]
    Beta3: [18, 25]
    HighBeta: [25, 30]
    Gamma: [30, 50]

These boundaries deserve explicit discussion, because they differ from some legacy conventions and the choice has clinical consequences.

Alpha: 8–13 Hz (Not 8–12)

The alpha band upper boundary was historically debated. Some systems used 12 Hz, placing the 12–13 Hz range in beta. The clinical standard—used by EEGLAB and the Kaiser convention—places alpha at 8–13 Hz. This is what the pipeline uses.

The distinction matters for sub-band analysis. Alpha2 (high alpha, 10.5–13 Hz) is associated with semantic processing and memory retrieval. Cutting alpha at 12 Hz loses the upper portion of this sub-band, which misrepresents high-alpha activity and inflates low-beta power. The 13 Hz boundary ensures that the full alpha range is captured, and that Beta1 (13–15 Hz, the sensorimotor rhythm range) is not contaminated with alpha activity.

Beta: 13–30 Hz (Not 12–25)

Similarly, the beta band runs from 13 Hz (immediately above alpha) to 30 Hz. Some older conventions used 12–25 Hz, which created a gap between 25 and 30 Hz that was either uncategorized or lumped into gamma. The 13–30 Hz range is the current clinical standard and ensures clean separation between alpha, beta, and gamma.

HighBeta: 25–30 Hz

High beta is separated as its own band for clinical significance—elevated 25–30 Hz activity is one of the more reliable markers of cortical hyperarousal, anxiety, and excessive self-monitoring. Embedding it within the broader beta band (13–30 Hz) would dilute this signal. The Three-Layer Clinical Model used by the Coherence Workstation treats high-beta as a distinct clinical indicator, so it gets its own band.

Sub-Bands

Alpha1 (8–10.5 Hz) and Alpha2 (10.5–13 Hz) subdivide the alpha band into attentional (low alpha) and semantic/memory (high alpha) components. Beta1 (13–15 Hz), Beta2 (15–18 Hz), and Beta3 (18–25 Hz) provide finer granularity within the broad beta range. These sub-bands are always computed alongside the main bands—they add clinical detail without replacing the standard band structure.

Aperiodic (1/f) Spectral Fitting

Raw power spectra contain two distinct components: periodic oscillatory peaks (the brain’s rhythmic activity—alpha, theta, beta) and an aperiodic background that follows a 1/f power law (power decreases with frequency along a characteristic slope). Traditional band-power analysis conflates these—a high “alpha power” measurement might reflect a strong alpha oscillation, or it might reflect a steep aperiodic slope that happens to be high in the alpha range.

The pipeline separates periodic from aperiodic components using specparam (formerly FOOOF—Fitting Oscillations & One Over F), a peer-reviewed spectral parameterization tool (Haller et al., 2018):

aperiodic:
  freq_range: [2, 40]
  r_squared_threshold: 0.85
  peak_width_limits: [1, 8]
  max_n_peaks: 6
  min_peak_height: 0.1
  peak_threshold: 2.0
  min_peak_spacing: 2.0
  min_relative_peak_power: 0.3

The Fitting Range: 2–40 Hz

The aperiodic fit operates on a narrower frequency range than the full PSD. The lower bound of 2 Hz avoids the high-pass filter’s transition band—below ~1.5 Hz, the filter attenuates the signal, creating an artificial spectral roll-off that would distort the aperiodic fit. The upper bound of 40 Hz avoids edge effects near the 50 Hz PSD ceiling and the 60 Hz notch filter. Within this 2–40 Hz window, the spectral shape is determined by the brain’s activity and not by filter artifacts.

What Specparam Returns

For each channel, specparam fits a model consisting of an aperiodic background (parameterized by offset and exponent) plus up to 6 Gaussian peaks representing periodic oscillations. The key outputs:

Offset is the power at 1 Hz on the aperiodic component—it reflects overall signal amplitude. Higher offset means more total power.

Exponent (slope) is the steepness of the 1/f decay. A steeper slope (higher exponent, typically 1.5–2.5) means the spectrum is dominated by low-frequency power. A flatter slope (lower exponent, 0.5–1.5) means relatively more high-frequency power. Clinically, the exponent reflects the brain’s excitation/inhibition balance—flatter slopes are associated with greater cortical excitation.

Peak frequencies and heights identify the periodic oscillations that stand out above the aperiodic background. A strong alpha peak might appear at 10 Hz with a height of 0.5 log-units above the aperiodic fit. These peaks represent genuine oscillatory activity, separated from the broadband aperiodic component.

R² fit quality measures how well the model fits the data. The threshold of 0.85 is the standard in the specparam literature—channels with R² below this are flagged as poor fits, which typically indicates excessive noise, artifact contamination, or atypical spectral shapes that the model can’t capture.

Secondary Peak Filtering

The min_relative_peak_power: 0.3 parameter prevents specparam from reporting trivial spectral bumps as oscillatory peaks. Any detected peak must have at least 30% of the power of the strongest peak in that channel’s spectrum. This reduces false-positive peak detections—small spectral irregularities that are noise rather than genuine oscillations.

Hemispheric Asymmetry

Asymmetry is computed for seven standard homologous electrode pairs:

homologous_pairs:
  - [F3, F4]
  - [C3, C4]
  - [P3, P4]
  - [T3, T4]
  - [T5, T6]
  - [F7, F8]
  - [O1, O2]

For each pair and each frequency band, the pipeline computes the log-ratio asymmetry index: ln(right power) − ln(left power). Positive values indicate right-hemisphere dominance; negative values indicate left-hemisphere dominance. The asymmetry threshold for clinical significance is 0.15 (from asymmetry.threshold: 0.15 in the configuration).

The log-ratio formula is standard in the literature (Allen, Coan, & Nazarian, 2004). Using logarithmic power rather than raw power normalizes for individual differences in absolute amplitude—a person with high overall alpha power and a person with low overall alpha power can have the same asymmetry index if the left-right ratio is the same.

What Asymmetry Means (and Doesn’t Mean)

Frontal alpha asymmetry (F3/F4) is one of the most studied EEG biomarkers, with a large literature linking rightward alpha asymmetry to approach motivation and leftward asymmetry to withdrawal. But asymmetry is also one of the most over-interpreted metrics in clinical QEEG. A single asymmetry value at a single electrode pair is not a diagnosis. It’s a data point that gains meaning only in the context of the full spectral profile, the connectivity architecture, and the clinical presentation.

The Coherence Workstation reports asymmetry as one layer of the analysis, not as a standalone finding. The analysis display integrates asymmetry with connectivity metrics, spectral power, and the organizational dynamics framework to provide a structural interpretation rather than a single-metric conclusion.

Conditions: Eyes Open and Eyes Closed

Spectral analysis is computed separately for eyes-open (EO) and eyes-closed (EC) conditions. The comparison between conditions is clinically informative: alpha power typically increases with eyes closed (the classic “alpha blocking” phenomenon), and the magnitude of this increase reflects the functional responsiveness of the visual-occipital system.

Each condition produces its own stage JSON file (spectral_resting_eo and spectral_resting_ec), with identical structure but different data. The desktop application presents both conditions with tab-based switching, allowing the clinician to compare spectral profiles across conditions.