%0 Journal Article
%T Multiple Harmonics Fitting Algorithms Applied to Periodic Signals Based on Hilbert-Huang Transform
%A Hui Wang
%A Zhengshi Liu
%A Bin Zhu
%A Quanjun Song
%J Journal of Sensors
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/580152
%X 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 ˇ°sinusoidal waveˇ± whose amplitude and phase are both transient, the ˇ°triangular waveˇ± 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 ˇ°triangular waveˇ± and the corresponding points of fitting ˇ°sinusoidal waveˇ± is marvelously small. That maybe means, under the circumstances of any periodic signal, that ENOBs of high-resolution ADC can be tested accurately. 1. Introduction For robot sensors, ADC plays a key role, which receives the signal coming from front-end circuit and then converts it into digital logic output [1, 2]. ADC testing frequently uses periodic signals to obtain most of the specification parameters, such as the ENOBs, signal-to-noise and distortion (SINAD) ratio, integral nonlinearity (INL), differential nonlinearity (DNL), and the transfer function. Sine fitting is a very efficient and fast way to help in the evaluation of most of these characteristic parameters. IEEE standards 1057 [3] and 1241 [4] present two methods that estimate three (amplitude, phase, and dc component) or four parameters (including also the frequency) of a sine wave that best fit a set of acquired samples. The two sine fitting methods described by IEEE standards are general and classical methods aiming at the data acquisition channel as well as the ADC demarcation. However, as for a sinusoidal sampling signal with harmonic distortion, whether using the classical three-parameter or four-parameter sine
%U http://www.hindawi.com/journals/js/2013/580152/