Lower bounds on the performance of Analog to Digital Converters
This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. We define the performance of an ADC as the worst-case average...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/72551 https://orcid.org/0000-0001-9088-0205 |
| _version_ | 1811083769885491200 |
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| author | Osqui, Mitra Megretski, Alexandre Roozbehani, Mardavij |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Osqui, Mitra Megretski, Alexandre Roozbehani, Mardavij |
| author_sort | Osqui, Mitra |
| collection | MIT |
| description | This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. We define the performance of an ADC as the worst-case average intensity of the filtered input matching error. The input matching error is the difference between the input and output of the ADC. This error signal is filtered using a shaping filter, the passband of which determines the frequency region of interest for minimizing the error. The problem of finding a lower bound for the performance of an ADC is formulated as a dynamic game problem in which the input signal to the ADC plays against the output of the ADC. Furthermore, the performance measure must be optimized in the presence of quantized disturbances (output of the ADC) that can exceed the control variable (input of the ADC) in magnitude. We characterize the optimal solution in terms of a Bellman-type inequality. A numerical approach is presented to compute the value function in parallel with the feedback law for generating the worst case input signal. The specific structure of the problem is used to prove certain properties of the value function that allow for iterative computation of a certified solution to the Bellman inequality. The solution provides a certified lower bound on the performance of any ADC with respect to the selected performance criteria. |
| first_indexed | 2024-09-23T12:38:46Z |
| format | Article |
| id | mit-1721.1/72551 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:38:46Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/725512022-10-01T10:14:14Z Lower bounds on the performance of Analog to Digital Converters Osqui, Mitra Megretski, Alexandre Roozbehani, Mardavij Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Megretski, Alexandre Osqui, Mitra Megretski, Alexandre Roozbehani, Mardavij This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with outputs taking values in a finite set. We define the performance of an ADC as the worst-case average intensity of the filtered input matching error. The input matching error is the difference between the input and output of the ADC. This error signal is filtered using a shaping filter, the passband of which determines the frequency region of interest for minimizing the error. The problem of finding a lower bound for the performance of an ADC is formulated as a dynamic game problem in which the input signal to the ADC plays against the output of the ADC. Furthermore, the performance measure must be optimized in the presence of quantized disturbances (output of the ADC) that can exceed the control variable (input of the ADC) in magnitude. We characterize the optimal solution in terms of a Bellman-type inequality. A numerical approach is presented to compute the value function in parallel with the feedback law for generating the worst case input signal. The specific structure of the problem is used to prove certain properties of the value function that allow for iterative computation of a certified solution to the Bellman inequality. The solution provides a certified lower bound on the performance of any ADC with respect to the selected performance criteria. United States. Army Research Office. Efficient Linearized All-Silicon Transmitter ICs 2012-09-06T18:21:29Z 2012-09-06T18:21:29Z 2012-03 2011-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-61284-799-3 978-1-61284-800-6 0743-1546 http://hdl.handle.net/1721.1/72551 Osqui, Mitra, Alexandre Megretski, and Mardavij Roozbehani. “Lower Bounds on the Performance of Analog to Digital Converters.” 50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC). 1036–1041. https://orcid.org/0000-0001-9088-0205 en_US http://dx.doi.org/10.1109/CDC.2011.6161525 50th IEEE Conference on Decision and Control and European Control Conference 2011 (CDC-ECC) Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Osqui, Mitra Megretski, Alexandre Roozbehani, Mardavij Lower bounds on the performance of Analog to Digital Converters |
| title | Lower bounds on the performance of Analog to Digital Converters |
| title_full | Lower bounds on the performance of Analog to Digital Converters |
| title_fullStr | Lower bounds on the performance of Analog to Digital Converters |
| title_full_unstemmed | Lower bounds on the performance of Analog to Digital Converters |
| title_short | Lower bounds on the performance of Analog to Digital Converters |
| title_sort | lower bounds on the performance of analog to digital converters |
| url | http://hdl.handle.net/1721.1/72551 https://orcid.org/0000-0001-9088-0205 |
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