Interpolation of Discrete-Time Series
Publication: Journal of Engineering Mechanics
Volume 146, Issue 6
Abstract
Interpolation can be used to up-sample a sparsely recorded or simulated data set. Ideal interpolation models such as a Nyquist-bandlimited filter in the frequency domain and sinc function in the time domain are difficult to implement. Previous researchers proposed an interpolation scheme that interpolates data faithfully and preserves the spectral features of the original data. This approach has one possible limitation that the interpolated data may not pass through the original data points exactly. This technical note provides a modification of this scheme to ensure the interpolated data capture the original data points.
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Acknowledgments
Support was provided in part by National Science Foundation (NSF) Grant No. 1562244.
References
Blu, T., P. Thevenaz, and M. Unser. 2004. “Linear interpolation revitalized.” IEEE Trans. Image Process. 13 (5): 710–719. https://doi.org/10.1109/TIP.2004.826093.
Comerford, L., I. A. Kougioumtzoglou, and M. Beer. 2016. “Compressive sensing based stochastic process power spectrum estimation subject to missing data.” Probab. Eng. Mech. 44 (Apr): 66–76. https://doi.org/10.1016/j.probengmech.2015.09.015.
Guo, Y. L., A. Kareem, Y. Q. Ni, and W. Y. Liao. 2012. “Performance evaluation of Canton Tower under winds based on full-scale data.” J. Wind Eng. Ind. Aerodyn. 104 (May): 116–128. https://doi.org/10.1016/j.jweia.2012.04.001.
Hou, H. S., and H. C. Andrews. 1978. “Cubic splines for image interpolation and digital filtering.” IEEE Trans. Acoust. Speech Signal Process. 26 (6): 508–517. https://doi.org/10.1109/TASSP.1978.1163154.
IEEE Digital Signal Processing Committee. 1979. Programs for digital signal processing. New York: IEEE.
Li, Y. 1988. “Stochastic response of a tension leg platform to wind and wave fields.” Ph.D. thesis, Dept. of Mechanical Engineering, Univ. of Houston.
Li, Y., and A. Kareem. 1990. “ARMA systems in wind engineering.” Probab. Eng. Mech. 5 (2): 50–59. https://doi.org/10.1016/0266-8920(90)90007-7.
Oetken, G., T. W. Parks, and H. W. Schüssler. 1975. “New results in the design of digital interpolators.” IEEE Trans. Acoust. Speech Signal Process. 23 (3): 301–309. https://doi.org/10.1109/TASSP.1975.1162686.
Qu, C.-X., T.-H. Yi, Y.-Z. Zhou, H.-N. Li, and Y.-F. Zhang. 2018. “Frequency identification of practical bridges through higher-order spectrum.” J. Aerosp. Eng. 31 (3): 04018018. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000840.
Saunders, L. R., and A. G. Collings. 1980. “Efficient solution of modal equations with arbitrary loadings.” Eng. Struct. 2 (1): 35–48. https://doi.org/10.1016/0141-0296(80)90027-9.
Turek, D. B. 2004. “Design of efficient digital interpolation filters for integer upsampling.” M.Eng. thesis, Dept. of Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
Wang, L. 2007. “Stochastic modeling and simulation of transient events.” Ph.D. thesis, Dept. of Civil Engineering and Geological Sciences, Univ. of Notre Dame.
Yang, X.-M., T.-H. Yi, C.-X. Qu, H.-N. Li, and H. Liu. 2019. “Automated eigensystem realization algorithm for operational modal identification of bridge structures.” J. Aerosp. Eng. 32 (2): 04018148. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000984.
Yang, Y., and S. Nagarajaiah. 2016. “Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure.” Mech. Syst. Signal Process. 74 (Jun): 165–182. https://doi.org/10.1016/j.ymssp.2015.11.009.
Yi, T.-H., X.-J. Yao, C.-X. Qu, and H.-N. Li. 2019. “Clustering number determination for sparse component analysis during output-only modal identification.” J. Eng. Mech. 145 (1): 04018122. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001557.
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Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 6 • June 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jan 17, 2019
Accepted: Dec 12, 2019
Published online: Mar 18, 2020
Published in print: Jun 1, 2020
Discussion open until: Aug 18, 2020
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