Zhang Zhenwei, VanSwearingen Jessie, Brach Jennifer S, Perera Subashan, Sejdić Ervin
Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA.
Department of Physical Therapy, University of Pittsburgh, Pittsburgh, PA 15260, USA.
Comput Biol Med. 2017 Jan 1;80:175-184. doi: 10.1016/j.compbiomed.2016.11.009. Epub 2016 Nov 26.
Human gait is a complex interaction of many nonlinear systems and stride intervals exhibiting self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a "biomarker" of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of 16 mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The 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.
人类步态是许多非线性系统的复杂相互作用，步幅间隔在长时间尺度上呈现自相似性，可被建模为分形过程。标度指数代表分形程度，可被解释为相关疾病的“生物标志物”。先前的研究表明，当应用于步幅间隔时间序列时，平均小波方法能提供最准确的结果来估计该标度指数。本文的目的是确定平均小波方法最合适的母小波。本文使用模拟和实际分形信号对16种母小波进行了比较数值分析。模拟分形信号是在不同信号长度和标度指数下生成的，这些标度指数表示一系列生理上可想象的分形信号。由于这五种小波在短信号和长信号的均方误差测试中表现良好，因此被选为候选小波。接下来，我们针对生理相关的步幅时间序列长度对这五种母小波进行了比较分析。我们的分析表明，symlet 2母小波对于长时间间隔具有低均方误差和低方差，对于短信号长度具有相对较低的误差。它可被视为最合适的母函数，而无需考虑信号长度。
