Paired time-series synchrony analysis

A delivered research contract. Two simultaneous multi-channel recordings of the same event, and one question: do the two signals move together.

I answered it twice. Cross-correlation and dynamic time warping share no assumptions. One looks for a shifted linear match, the other for the cheapest alignment path. Running both and then testing whether they converge is the difference between a result and a claim. Most analysis stops after the first method.

The scale was 7,991a paired computations over 714,474 samples per channel set, sampled at 7.81 Hz, bandpassed from 0.01 to 0.1 Hz with a fourth-order zero-phase Butterworth filter, then read through a 30-second rolling window.

The delivery is the part I would show first. The first version was one notebook of 119a cells. It ran, and it was the wrong shape for the person receiving it. So it became four notebooks that each open cold, run alone, and hand the next one a saved array rather than a live kernel. Every code cell is preceded by an explanation of the reasoning rather than the syntax. The client was a researcher, not an engineer, and a deliverable they cannot open is not a deliverable.

It shipped with an explicit list of what the analysis could not resolve. They had not asked for that section.

The research is unpublished, so no finding appears here.