# Most suitable mother wavelet for the analysis of fractal properties of stride interval via the average wavelet coefficient method

zhenwei, zhang (2016) Most suitable mother wavelet for the analysis of fractal properties of stride interval via the average wavelet coefficient method. Master's Thesis, University of Pittsburgh. (Unpublished)

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## Abstract

The human gait is a complex interaction of many nonlinear systems and stride intervals that can be modeled as a stochastic $1/f^\beta$ process, where the spectral index $\beta$ can be interpreted as a “biomarker” of diseases. The previous study showed that the average wavelet method provides the most accurate results when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for analysis of the fractal characteristics of the stride interval time series.
This paper presents a comparative numerical analysis of sixteen mother wavelets applied to the average wavelet coefficient method with different simulated signal lengths and $\beta$ values. Five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths . Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length.

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## Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
zhenwei, zhangzhz87@pitt.eduZHZ870000-0001-7215-0858
ETD Committee:
Committee ChairErvin, SejdicESEJDIC@pitt.edu
Committee MemberHai, LiHAL66@pitt.edu
Committee MemberMurat, AkcakayaAKCAKAYA@pitt.edu
Date: 15 September 2016
Date Type: Publication
Defense Date: 8 July 2016
Approval Date: 15 September 2016
Submission Date: 21 July 2016
Access Restriction: 5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
Number of Pages: 52
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Electrical Engineering
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: fractals,time series analysis, self similarity, gait, stride intervals, wavelets , 1/f process, mother wavelet
Date Deposited: 15 Sep 2016 19:53