Hermite expansions of compact support waveforms: applications to myoelectric signals

Abstract

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.

An Adaptive Detector of Genioglossus EMG Reflex Using Berkner Transform for Time Latency Measurement in OSA Pathophysiological Studies

“…In fact, they used a matched CWT, based on a mother wavelet chosen according to the MUAP shape. The method used the fact that in the context of single differential EMG recording, the first-order Hermite-Rodriguez function is well suited to describe the basic MUAP shape [22] and thus to construct the mother wavelet. The range of the scale parameter is chosen in order to obtain wavelet support within the physiological MUAP durations.…”

Simulation system of spinal cord motor nuclei and associated nerves and muscles, in a Web-based architecture

“…(11), (12) and (13); and F(n) is the total muscle force. The motor-unit action potentials (MUAPs) were modeled using Hermite-Rodriguez functions, which fit the shape of MUAPs well (Lo Conte et al 1994;Zhou and Rymer 2004). Surface bipolar electrodes were assumed, with 8 mm diameters and 20 mm separation, as typically used in human experiments.…”

Simultaneous Time-Frequency Modeling of Ultra-Wideband Antennas by Two-Dimensional Hermite Processing

“…The extreme values of a Hermite function exhibits near equal amplitudes which is a rather useful feature to model close-to-the-edge field singularities and large radiating objects such as arrays. Beside this choice, also the Hermite Rodriguez functions [17] could be considered for the interpolation of compact-support images, but it has been verified that the corresponding interpolation converges not uniformly and slower [12] than the AHF2 and that the interpolation accuracy is more sensible to the scale factor than in the case of AHF2.…”