Signal Example — ICA 2: What Is a Mixture?

Often in EEG analysis, we fall into the trap of thinking about a specific channel (like Fz or Oz) as measuring a specific brain area. But due to physics, the electrical potentials generated by the brain smear and conduct across the scalp.

What you record at an electrode isn't a single "source" — it is a mixture of many sources added together.

This is Part 2 of the ICA pedagogical sequence. It formally proves why we need an algorithm to separate our data.

The Forward Problem

This demonstration creates two distinct underlying components:

1. Source 1: A healthy brain oscillation (alpha/spindle bursts).

2. Source 2: A massive blink artifact.

This minimalist demo serves as a sandbox to prove that an electrode is not a brain signal; it is a mixture.

You can adjust the Mix Balance slider to smoothly sweep from seeing 100% pure brain signal, to a 50/50 mix, all the way to 100% blink artifact. This proves exactly how a single scalp electrode physically crossfades and scales electrical potentials based on distances and conductivities. This creates the exact "forward-problem" that ICA aims to solve backward!

Code

using EegFun
EegFun.signal_example_ica_mixture()

See Also

• Part 1: Matrix Math Basics — What is an Unmixing Matrix?

• Part 3: Mixing & Unmixing — Two electrodes, mixing matrices, and the ICA algorithm

• Part 4: 3 Sources & Scatter Geometry — Advanced: rotation geometry, scatter plots, kurtosis

• Part 5: Sphering (Whitening) — Why ICA optimization is just finding an angle

• Part 6: Inside the Black Box — How the Gradient Ascent math actually loops