Event-Related Potentials (ERP) Simulator & Explorer

Interactive Averaging Simulation

Trials ($N$): 0

$\text{Amplitude } (\mu\text{V})$

Individual Trials (Noise) Running Average True Target ERP

Stimulus Onset ($t = 0\text{ ms}$) $100\text{ ms}$ $200\text{ ms}$ $300\text{ ms}$ $400\text{ ms}$ $500\text{ ms}$

Stimulus Presentation Actions

Simulation Variables

Noise Amplitude (Background EEG): 20 µV

Signal Amplitude (True ERP): 5 µV

Raw Signal-to-Noise Ratio (SNR) 1 : 4.00 $\text{Ratio} = \frac{\text{Signal}}{\text{Noise}}$ before averaging

Noise Reduction Factor 1.00x Proportional to $1 / \sqrt{N}$

Estimated Post-Average SNR 0.25 $\text{SNR}_{\text{post}} = \text{SNR}_{\text{raw}} \cdot \sqrt{N}$

Ongoing EEG Recorder Timeline

Streaming Channel #64

Continuous Sweep Speed: 1.0s/div

The Epoching Process: The scrolling trace above represents the raw background brain rhythm. The red dashed lines represent auditory stimulus onset triggers ($S_1, S_2, \dots$). The signal averager isolates local epochs (time window highlighted by a shaded rectangle) locked directly to these trigger times to run calculations below.

A complete human Event-Related Potential (ERP) consists of sequential components categorized by their latency (time delay post-stimulus). Hover or click on the labeled peaks to explore their neurological origins:

Interactive Schematic

Amplitude ($\mu\text{V}$) is inverted (- is UP)

Selected ERP Component 40 - 60 ms

Cortical P1 (P50 Wave)

An early sensory positive component reflecting initial processing in the primary auditory cortex. It is often used to study sensory gating (e.g., the brain's ability to filter out redundant auditory information).

The Signal-to-Noise Problem

Background EEG activity (alpha, beta, delta, theta waves) typically ranges between $20\,\mu\text{V}$ and $100\,\mu\text{V}$. In contrast, cognitive sensory ERPs are buried at values between $1\,\mu\text{V}$ and $10\,\mu\text{V}$. Individual stimulus trials look identical to random background noise.

The Averaging Formulation

An ongoing recording is divided into stimulus-locked trials $S_j(t) = s(t) + n_j(t)$, where $s(t)$ is the consistent time-locked ERP wave (signal), and $n_j(t)$ is the random uncorrelated noise (background EEG) on trial $j$.

$$\text{Average}(t) = \frac{1}{N} \sum_{j=1}^{N} S_j(t) = s(t) + \frac{1}{N}\sum_{j=1}^{N} n_j(t)$$

Mathematical Noise Suppression

Assuming the background EEG noise $n_j(t)$ is Gaussian with a mean of zero and variance of $\sigma^2$, and is completely uncorrelated across trials, the variance of the averaged noise goes down with $N$ trials:

$$\sigma_{\text{average}} = \frac{\sigma}{\sqrt{N}}$$

Thus, with 100 trials, background noise is suppressed by a factor of $\sqrt{100} = 10$, bringing a $20\,\mu\text{V}$ noise down to a manageable $2\,\mu\text{V}$, revealing the pure sensory ERP.

Faraday Cage Shielding Active Differential Amplifiers: $N = 64$

Interactive Noise Reduction Theorem

By adjusting the sliders, you change the parameters of the simulation in real time. Standard clinical recordings aim for a target post-average Signal-to-Noise Ratio (SNR) of at least $1.5$ to $2.0$ to make safe clinical judgments.

$\text{Target ERP Signal}$ 5.0 µV

$\text{Background EEG Noise Level} / \sqrt{N}$ 20.0 µV

Calculated Quality Factor: Unsatisfactory