Features in Signals

Copyright 2026 James B. Wilson, Colorado State University

US Geological Survey Data May 26, 2002

What makes Earthquake signals distinct? (Describe some features)

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Earth quake

Geologist observe earth quakes start small (P-wave) then get a bigger wave (S-Wave)

Think of accumulating all the little changes to make an integral that would explain the start of a P-wave, then an S-wave

Adapting you measure

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Using choices of \(\kappa\) what might you learn?

Let \(\sigma(t)\) be the signal at time \(t\)

You choose a window and a function \(\kappa\) where this is a big number when the signal starts.

\[\nu(s):=\int_{start}^{stop} |\sigma(t) \kappa(s,t)| dt\]