n:m Coherence

Demonstration of n:m coherence for AAS 2025 conference paper

The n:m Coherence statistic is a variation of the ordinary magnitude-squared coherence, that accounts for a frequency multiplication between an input and output signal. The ordinary magnitude-squared coherence calculates a value between 0 and 1 that is indicative of the causality between an input and output signal, when there is a linear (1:1) relationship between the frequency components in the input signal and the output signal. For example, if there is a tonal signal at 100 Hz in the input signal, and there is a tonal signal of 100 Hz in the output signal, it is likely the ordinary magnitude-squared coherence will be close to 1. However, if the output had a tonal signal at 200 Hz, instead of 100 Hz, the ordinary magnitude-squared coherence would be 0. By using the n:m coherence metric, the coherence can be determined.

This Matlab code accompanies the conference paper:

Howard, C.Q. (2025), 'N:M Coherence for determining the causality of a transfer function with a non-linear frequency relationship', Proceedings of ACOUSTICS 2025, 12-14 November 2025, Joondalup, Australia

and shows examples of the n:m coherence metric in incremental complexity.