发表机构
University of Nebraska Medical Center; University of Iowa Hospitals and Clinics（内布拉斯加医学中心; 爱荷华大学医院与诊所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出用高阶谱（HOS）及调制图（modulogram）分析生理信号的调制，可规避滤波偏差与高斯噪声非高斯化问题，还结合HOSD提升识别能力，通过盲检测β波爆发验证效果。
AI 中文摘要
在生理信号分析中，经常需要识别频谱功率的调制。通过滤波和包络提取估计相关频段的功率存在若干局限：滤波器的选择可能使任何最终估计产生偏差，而加性高斯噪声会因包络计算的非线性变为非高斯噪声。本研究探讨高阶累积量的频谱分解（即高阶谱，HOS）如何规避这些局限，重点关注双谱在识别调制振荡中的应用。具体而言，研究表明：1）将双谱视为维格纳-维尔分布的互谱时，可将其解释为跨频率功率线性依赖的度量；2）双谱的特定二维子域可用于识别调制载波，在避免完整双谱估计的立方复杂度的同时，恢复调制信号与载波信号的基本频谱特性，该子域的表示形式——调制图（modulogram）被证明是识别和区分不同调制形式的工具；3）作为基于累积量的度量，调制图不受加性高斯噪声的偏差影响；4）调制图相位保留了可识别调制时间模式的信息；5）近期提出的高阶谱加性分解方法（HOSD）应用于双谱时，进一步助力识别。这些进展通过盲检测啮齿动物和人类局部场电位记录中的β波爆发得到例证。最后，探讨了本方法与此前通过矩最大化进行盲识别（BI）的技术（包括盲反卷积和独立成分分析）之间的关系。
英文摘要
A need to identify modulation of spectral power arises frequently in the analysis of physiological signals. Estimation of power in the relevant bands through filtering and envelope extraction has several limitations: the choice of filter may bias any resulting estimate, while additive Gaussian noise becomes non-Gaussian due to the nonlinearity of envelope computation. The present work considers how spectral decompositions of higher-order cumulants (higher-order spectra, HOS) avoid these limitations, with an emphasis on the use of the trispectrum to identify modulated oscillations. Specifically, it is shown: 1) The trispectrum may be interpreted as a measure of linear dependencies of power across frequencies by viewing it as the cross spectrum of the Wigner-Ville distribution. 2) A particular two-dimensional subdomain of the trispectrum is useful for identifying modulated carriers, recovering essential spectral properties of both the modulating and carrier signals while avoiding the cubic complexity of full trispectrum estimation. A representation of this subdomain, the modulogram, is demonstrated as a tool for identifying and distinguishing different forms of modulation. 3) As a cumulant-derived measure, the modulogram is not biased by additive Gaussian noise. 4) Modulogram phase retains information by which temporal patterns of modulation may be identified. 5) A recently described additive decomposition of HOS (HOSD) further aids identification when applied to the trispectrum. These developments are illustrated with the blind detection of beta bursts in rodent and human local field potential recordings. Finally, the relationship between the present approach and prior techniques of blind identification (BI) through moment maximization, including blind deconvolution and independent component analysis, is considered.
Comments42 pages, 10 figures. A previous version of this preprint was published under the title "A Slice of Trispectrum for Patterns of Modulation" at https://doi.org/10.36227/techrxiv.21401703.v1
