EegFun

Appearance

Signal Example — Mixing & Unmixing (Beginner ICA) ​

Interactive demonstration of signal mixing and ICA unmixing.

The Cocktail Party Problem ​

Imagine you're at a party with two people talking. You have two microphones, but each one picks up both voices — just at different volumes depending on how close each person is to each mic.

That's exactly what happens with EEG:

  • Your brain generates an electrical signal

  • Your eyes produce large signal changes every time you blink

  • Each electrode on your scalp picks up a mixture of both

The result? Every electrode's recording is a jumbled combination of brain activity and blink artifacts. You never see the clean sources directly.

ICA (Independent Component Analysis) is the algorithm that untangles the mixture back into the original sources — like being able to isolate each person's voice from the party recording.

What This Demo Shows ​

ColumnWhat you see
Left — "What's really happening"The two true source signals: a brain oscillation and eye blink artifacts
Middle — "What electrodes record"The mixed signals, with the mixing equation shown in the title (e.g. E1 = 1.00 × Brain + 0.50 × Blink)
Right — "What ICA recovers"The unmixed signals recovered by ICA

Below the plots, three panels show the Matrix Equations:

  1. Mixing M: How sources S become electrodes E (M × S = E).

  2. Exact Inverse M⁻¹: The mathematically perfect "reverse recipe".

  3. Your Weights / ICA Found: The current unmixing recipe being applied.

Things to Try ​

Step 1: See the Problem ​

  1. Set Mix Amount to 0.5. Look at the middle column — the blink spikes are now mixed into the brain electrode (E1), and brain oscillations contaminate the blink electrode (E2).

  2. Look at the Mixing M panel. It's a colored 2×2 grid showing exactly how much each source bleeds into each electrode.

Step 2: Try to Fix It Yourself ​

  1. Use the "Subtract E2 from E1" slider. You're trying to remove the blink contamination from electrode 1 by subtracting a scaled version of electrode 2.

  2. Watch the Shape Match — can you get to 100%? It's surprisingly hard!

  3. Notice that even if you get 100% Shape, the Amplitude Match might be low. This is because a simple subtraction doesn't correctly invert the whole mixing matrix.

Step 3: Let ICA Do It ​

  1. Click Unmix! — ICA finds the optimal 2×2 matrix automatically.

  2. Watch the manual sliders jump to the values ICA found — now you can see exactly what weights it used.

  3. Compare the ICA Found Matrix with the Exact Inverse M⁻¹ — ICA essentially "reverse engineered" the mixing recipe without ever seeing the original sources!

Controls ​

ControlRangeDescription
Mix Amount0–1How much the sources bleed across electrodes
Brain Freq4–20 HzFrequency of the oscillatory brain signal
Blink Size0.5–5Amplitude of eye blink artifacts
Noise0–1Additive sensor noise
Subtract E2→E10–1.5Manual unmixing: remove E2 contribution from E1
Subtract E1→E20–1.5Manual unmixing: remove E1 contribution from E2
Unmix!—Run ICA to find optimal unmixing weights
Reset—Clear all unmixing

Why Does ICA Work? ​

ICA relies on one key insight: brain signals and eye blinks are statistically independent — knowing the state of one tells you nothing about the state of the other.

The Central Limit Theorem says that mixing independent, non-Gaussian sources always produces something more Gaussian (more random-looking) than either source alone. ICA exploits this in reverse: it searches for the unmixing matrix that makes the outputs as non-Gaussian as possible — which turns out to be equivalent to making them statistically independent.

This demo shows that unmixing is just **Matrix Inversion** — see also the [ICA (Blind Source Separation) demo](signal_example_ica.md).

See Also ​

Code ​

julia
using EegFun
EegFun.signal_example_mixing()