Complex Orthogonal Decomposition (C.O.D.) using Python

TL;DR

This paper demonstrates the application of Complex Orthogonal Decomposition (C.O.D.) to analyze oscillatory spatio-temporal signals, emphasizing phase information and unknown spatial forms, with Python implementations.

Contribution

It introduces a Python-based implementation of C.O.D. for signal analysis, including theoretical background and practical examples.

Findings

C.O.D. effectively extracts spatial and temporal modes from signals.

The method is well-suited for oscillatory signals with unknown spatial structures.

Python scripts demonstrate the efficiency and features of C.O.D.

Abstract

This work presents the application of the Complex Orthogonal Decomposition (C.O.D.) to a simple spatio-temporal signal. C.O.D. has been introduced rst in the article of B. Feeny, entitled "A Complex Orthogonal Decomposition for Wave Motion Analysis" [1], published in the Journal of Sound and Vibration. The purpose of this signal analysis method is to extract spatial and temporal modes out of a signal. This approach is especially suited to deal with oscillatory signals where phase information is important and where spatial forms are unknown. We provide two theoretical chapters presenting the main mathematical concepts behind C.O.D. and a series of example (with associated Python scripts) to demonstrate the e ciency of the method and some characteristical features.