Date of Award

Winter 2019

Project Type

Thesis

Program or Major

Electrical and Computer Engineering

Degree Name

Master of Science

First Advisor

Richard Messner

Second Advisor

Kent Chamberlin

Third Advisor

Nicholas Kirsch

Abstract

This thesis presents a system which can be used to generate Intrinsic Mode Functions and the associated Hilbert spectrum resulting from techniques based on the Empirical Mode Decomposition as pioneered by N. E. Huang at the end of the 20th century. Later dubbed the Hilbert-Huang Transform by NASA, the process of decomposing data manually through repetitive detrending and subtraction followed by applying the Hilbert transform to the results was presented as a viable alternative to the wavelet transform which was gaining traction at the time but had shown significant limitations. In the last 20 years, the Hilbert-Huang Transform has received a lot of attention, but that attention has been miniscule relative to the amount of attention received by wavelet transformation. This is, in part, due to the limitations of the Empirical Mode Decomposition and also in part due to the difficulty in developing a theoretical basis for the manner in which the Empirical Mode Decomposition works. While the question of theoretical foundations is an important and tricky one, this thesis presents a system that breaks many of the previously known limits on band-width resolution, mode mixing, and viable decomposable frequency range relative to sampling frequency of the Empirical Mode Decomposition.

Many recent innovations do not simply improve on N. E. Huang’s algorithm, but rather provide new approaches with different decompositional properties. By choosing the best technique at each step, a superior total decomposition can be arrived at. Using the Hilbert-Huang Transform itself during the decomposition as a guide as suggested by R. Deering in 2005, the final HHT can show distinct improvements. The AHHT System utilizes many of the properties of various Empirical Mode Decomposition techniques from literature, includes some novel innovations on those techniques, and then manages the total decomposition in an adaptive manner.

The Adaptive Hilbert-Huang Transform System (AHHT) is demonstrated successfully on many different artificial signals, many with varying levels of noise down to -5dB SNR, as well as on an electrocardiogram and for comparison with a surface electromyographic study which found biopotential frequency-shifting associated with the fatigue of fast-twitch muscle fibers.

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