Lo Conte L R, Merletti R, Sandri G V
Politecnico di Torino, Italy.
IEEE Trans Biomed Eng. 1994 Dec;41(12):1147-59. doi: 10.1109/10.335863.
Nonstationary signals with finite time support are frequently encountered in electrophysiology and other fields of biomedical research. It is often desirable to have a compact description of their shape and of their time evolution. For this purpose, Fourier analysis is not necessarily the best tool. The Hermite-Rodriguez and Associated Hermite basis functions are applied in this work. Both are based on the product of Hermite polynomials and Gaussian functions. Their general properties relevant to biomedical signal processing are reviewed. Preliminary applications are described concerning the analysis and description of: a) test signals such as a square pulse and a single cycle of a sinewave, b) electrically evoked myoelectric signals, and c) power spectra of either voluntary or evoked signals. It is shown that expansions with only five to ten terms provide an excellent description of the computer simulated and real signals. It is shown that these two families of Hermite functions are well suited for the analysis of nonstationary biological evoked potentials with compact time support. An application to the estimation of scaling factors of electrically evoked myoelectric signals is described. The Hermite functions show advantages with respect to the more traditional spectral analysis, especially in the case of signal truncation due to stimulation with interpulse intervals smaller than the duration of the evoked response. Finally, the Hermite approach is found to be suitable for classification of spectral shapes and compression of spectral information of either voluntary or evoked signals. The approach is very promising for neuromuscular diagnosis and assessment because of its capability for information compression and waveform classification.
具有有限时间支持的非平稳信号在电生理学和生物医学研究的其他领域中经常遇到。通常希望对其形状及其随时间的演变进行简洁的描述。为此，傅里叶分析不一定是最佳工具。在这项工作中应用了埃尔米特 - 罗德里格斯基函数和相关埃尔米特基函数。两者都基于埃尔米特多项式与高斯函数的乘积。回顾了它们与生物医学信号处理相关的一般特性。描述了关于以下方面的分析和描述的初步应用：a）测试信号，如方波和正弦波的单个周期，b）电诱发肌电信号，以及c）自主或诱发信号的功率谱。结果表明，仅用五到十项展开就能对计算机模拟信号和真实信号进行出色的描述。结果表明，这两类埃尔米特函数非常适合分析具有紧凑时间支持的非平稳生物诱发电位。描述了其在估计电诱发肌电信号缩放因子方面的应用。与更传统的频谱分析相比，埃尔米特函数显示出优势，特别是在由于脉冲间隔小于诱发反应持续时间的刺激而导致信号截断的情况下。最后，发现埃尔米特方法适用于对自主或诱发信号的频谱形状进行分类和频谱信息的压缩。由于其信息压缩和波形分类能力，该方法在神经肌肉诊断和评估方面非常有前景。
