Article
Measuring displacement signal with an accelerometer
Journal of Mechanical Science and Technology (Impact Factor: 0.84). 06/2010; 24(6):13291335. DOI: 10.1007/s1220601003361
ABSTRACT
An effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed in this paper.
To reconstruct displacement signal by means of doubleintegrating the time domain acceleration signal, the Nyquist frequency
of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal.
On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant
frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along
the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure
and record the original signal, reconstructing highfrequency signals in the time domain and reconstructing lowfrequency
signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included
in the sampling process, lowfrequency components of the signals are overestimated when displacement signals are reconstructed
from the Fourier transform of the acceleration signal. The proposed method utilizes curvefitting around the significant frequency
components of the Fourier transform of the acceleration signal before it is inverseFourier transformed. Curvefitting around
the dominant frequency components provides much better results than simply ignoring the insignificant frequency components
of the signal.
KeywordsAcceleration signalCurvefittingDisplacement signalInverse Fourier transformNyquist frequencySampling rate
To reconstruct displacement signal by means of doubleintegrating the time domain acceleration signal, the Nyquist frequency
of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal.
On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant
frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along
the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure
and record the original signal, reconstructing highfrequency signals in the time domain and reconstructing lowfrequency
signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included
in the sampling process, lowfrequency components of the signals are overestimated when displacement signals are reconstructed
from the Fourier transform of the acceleration signal. The proposed method utilizes curvefitting around the significant frequency
components of the Fourier transform of the acceleration signal before it is inverseFourier transformed. Curvefitting around
the dominant frequency components provides much better results than simply ignoring the insignificant frequency components
of the signal.
KeywordsAcceleration signalCurvefittingDisplacement signalInverse Fourier transformNyquist frequencySampling rate
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 "Determining relative displacements can be accomplished by several methodologies. The most common method is the double integration of the acceleration by a rectangular or trapezoidal rule (Sangbo, 2010). Generally, this problem can be described by the formula "
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