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Journal of Sensors
Volume 2013, Article ID 580152, 9 pages
Research Article

Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform

1Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei 230031, China
2Institute of Sound and Vibration Research, Hefei University of Technology, Hefei 230009, China
3Electronic Engineering Institute, Hefei 230037, China

Received 21 March 2013; Accepted 24 April 2013

Academic Editor: Aiguo Song

Copyright © 2013 Hui Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, such as kinds of sensors, analog-to-digital and digital-to-analog converters, and digital signal processing techniques, that are able to substitute typical discrete instruments like multimeters and analyzers. Signal-processing applications frequently use least-squares (LS) sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies: the Fourier series. This paper describes a new sine fitting algorithm that is able to fit a multiharmonic acquired periodic signal. By means of a “sinusoidal wave” whose amplitude and phase are both transient, the “triangular wave” can be reconstructed on the basis of Hilbert-Huang transform (HHT). This method can be used to test effective number of bits (ENOBs) of analog-to-digital converter (ADC), avoiding the trouble of selecting initial value of the parameters and working out the nonlinear equations. The simulation results show that the algorithm is precise and efficient. In the case of enough sampling points, even under the circumstances of low-resolution signal with the harmonic distortion existing, the root mean square (RMS) error between the sampling data of original “triangular wave” and the corresponding points of fitting “sinusoidal wave” is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately.