# Ranking power spectra: a proof of concept

## TL;DR

This paper introduces a novel method to analyze the order structure of power spectra in signals, providing descriptors that distinguish signals with identical spectral entropy, with applications in brain and muscle signal analysis.

## Contribution

The paper proposes two new descriptors that capture the order structure of power spectra, enhancing signal analysis beyond traditional spectral entropy measures.

## Key findings

- Significant differences in descriptors observed in brain and EMG signals across conditions.
- Descriptors effectively detect changes related to physiological and pathological states.
- Potential application in seizure detection and speech endpoint detection.

## Abstract

Objective: To characterize the irregularity of the spectrum of a signal, spectral entropy is a widely adopted measure. However, such a metric is invariant under any permutation of the estimations of the powers of individual frequency components on a predefined grid. This erases the order structure inherent in the spectrum which is also an important aspect of irregularity of the signal. To disentangle the order structure and extract meaningful information from raw digital signal, novel analysis method is necessary. Approach: A novel method to depict the order structure by simply ranking power estimations on frequency grid of a evenly spaced signal is proposed. Two descriptors mapping real- and vector-valued power spectrum estimation of a signal into scalar value are defined in a heuristic manner. By definition, the proposed descriptor is capable of distinguishing signals with identical spectrum entropies. Main Results: The proposed descriptor showed its potential in diverse problems. Significant (p<0.001) differences were observed from brain signals and surface electromyography of different pathological/physiological states. Drastic change accompanied by the alteration of the underlying process of signals enables it as candidate feature for seizure detection and endpoint detection in speech signal. Significance: This letter explores the previously ignored order structure in the spectrum of physiological signal. We take one step forward along this direction by proposing two computationally efficient descriptors with guaranteed information gain. As far as the authors are concerned, this is the first work revealing the effectiveness of the order structure in the spectrum in physiological signal processing.

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Source: https://tomesphere.com/paper/1905.11003