Signal Reconstruction via $H^{\infty}$ Sampled-Data Control Theory—Beyond the Shannon Paradigm
Open accessAbstract
This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H∞performance criterion naturally takes inter-sample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction.
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The perfect band-limiting assumption implies that the H2 suboptimal filter is given as an approximant of the ideal low-pass filter, which induces large errors in the time domain.
“The second is that the perfect band-limiting assumption (1) implies that the H 2 suboptimal filter is given as an approximant of the ideal low-pass filter [41], which induces large errors in the time domain [27].”
From $H^{\infty}$-Optimal Fractional Delay Filters (2013) · cites this paper as [27]
The obtained filter shows greater robustness against unknown disturbances due to the uniform attenuation of the error frequency response.
“Furthermore, the obtained filter shows greater robustness against unknown disturbances due to the nature of the uniform attenuation of the error frequency response; see [27] for details.”
From $H^{\infty}$-Optimal Fractional Delay Filters (2013) · cites this paper as [27]
Cites
Image quality assessment: from error visibility to structural similarity
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.819861 · Cited by 57,892 · see citing works
Optimal Sampled-Data Control Systems
Chen, T., & Francis, B. A. (1995) · doi:10.1007/978-1-4471-3037-6 · Cited by 2,217 · see citing works
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$H^{\infty}$-Optimal Fractional Delay Filters
Nagahara, M., & Yamamoto, Y. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2265678 · Cited by 15 · see citing works
Self-citation
- Authors
- Yamamoto, Y., Nagahara, M., & Khargonekar, P. P.
- Affiliations
- Kyoto University (JP)
- University of Florida (US)
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2012-02
- Volume
- 60
- Issue
- 2
- Pages
- 613-625
- ISSN
- 1053-587X (ISSN-L)
- 1941-0476
- OpenAlex
- W2004195823
- Cited by
- 49
- References
- 2
- Citations by year
- 2025: 1 · 2024: 4 · 2022: 4 · 2021: 5 · 2020: 1 · 2019: 7 · 2018: 5 · 2017: 3 · 2016: 3 · 2015: 4 · 2014: 3 · 2013: 6 · 2012: 3
- FWCI
- 6.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Signal Processing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science (22656095, 22760317)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Keywords
- signal reconstruction, audio reconstruction, image reconstruction
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