On the accuracy and resolution of powersum-based sampling methods
Recently, several sampling methods suitable for signals that are sums of Diracs have been proposed. Though they are implemented through different acquisition architectures, these methods all rely on estimating the parameters of a powersum series. We derive Cramer-Rao lower bounds (CRBs) for estimati...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/52382 |
| _version_ | 1826189770581082112 |
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| author | Kusuma, Julius Goyal, Vivek K. |
| 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 Kusuma, Julius Goyal, Vivek K. |
| author_sort | Kusuma, Julius |
| collection | MIT |
| description | Recently, several sampling methods suitable for signals that are sums of Diracs have been proposed. Though they are implemented through different acquisition architectures, these methods all rely on estimating the parameters of a powersum series. We derive Cramer-Rao lower bounds (CRBs) for estimation of the powersum poles, which translate to the Dirac positions. We then demonstrate the efficacy of simple algorithms due to Prony and Cornell for low-order powersums and low oversampling relative to the rate of innovation. The simulated performance illustrates the possibility of superresolution reconstruction and robustness to correlation in the powersum sample noise. |
| first_indexed | 2024-09-23T08:22:01Z |
| format | Article |
| id | mit-1721.1/52382 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:22:01Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/523822022-09-30T09:10:24Z On the accuracy and resolution of powersum-based sampling methods Kusuma, Julius Goyal, Vivek K. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Goyal, Vivek K. Goyal, Vivek K. Recently, several sampling methods suitable for signals that are sums of Diracs have been proposed. Though they are implemented through different acquisition architectures, these methods all rely on estimating the parameters of a powersum series. We derive Cramer-Rao lower bounds (CRBs) for estimation of the powersum poles, which translate to the Dirac positions. We then demonstrate the efficacy of simple algorithms due to Prony and Cornell for low-order powersums and low oversampling relative to the rate of innovation. The simulated performance illustrates the possibility of superresolution reconstruction and robustness to correlation in the powersum sample noise. Texas Instruments Leadership University Consortium Program NEC Corporation Fund for Research in Computers and Communications IEEE Signal Processing Society 2010-03-08T18:08:57Z 2010-03-08T18:08:57Z 2009-01 2008-09 Article http://purl.org/eprint/type/JournalArticle 1053-587X http://hdl.handle.net/1721.1/52382 Kusuma, J., and V.K. Goyal. “On the Accuracy and Resolution of Powersum-Based Sampling Methods.” Signal Processing, IEEE Transactions on 57.1 (2009): 182-193. © 2008 IEEE en_US http://dx.doi.org/10.1109/TSP.2008.2007102 IEEE Transactions on Signal Processing Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Kusuma, Julius Goyal, Vivek K. On the accuracy and resolution of powersum-based sampling methods |
| title | On the accuracy and resolution of powersum-based sampling methods |
| title_full | On the accuracy and resolution of powersum-based sampling methods |
| title_fullStr | On the accuracy and resolution of powersum-based sampling methods |
| title_full_unstemmed | On the accuracy and resolution of powersum-based sampling methods |
| title_short | On the accuracy and resolution of powersum-based sampling methods |
| title_sort | on the accuracy and resolution of powersum based sampling methods |
| url | http://hdl.handle.net/1721.1/52382 |
| work_keys_str_mv | AT kusumajulius ontheaccuracyandresolutionofpowersumbasedsamplingmethods AT goyalvivekk ontheaccuracyandresolutionofpowersumbasedsamplingmethods |