Sampling and reconstruction of sparse signals in fractional fourier domain
Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain--a transformation which generalizes the conventional Fourier transform has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem...
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| Format: | Journal Article |
| Language: | English |
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2010
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| Online Access: | https://hdl.handle.net/10356/92280 http://hdl.handle.net/10220/6497 |
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| author | Ayush Bhandari Pina Marziliano |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Ayush Bhandari Pina Marziliano |
| author_sort | Ayush Bhandari |
| collection | NTU |
| description | Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain--a transformation which generalizes the conventional Fourier transform has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem for fractional bandlimited (or fractional Fourier bandlimited) signals are the same as for the Fourier domain case i.e. sampling (and reconstruction) in FrFT domain can be seen as an orthogonal projection of a signal onto a subspace of fractional bandlimited signals. As neat as this extension of Shannon's framework is, it inherits the same fundamental limitation that is prevalent in the Fourier regime-what happens if the signals have singularities in the time domain (or the signal has a nonbandlimited spectrum)? In this paper, we propose a uniform sampling and reconstruction scheme for a class of signals which are nonbandlimited in FrFT sense. Specifically, we assume that samples of a smoothed version of a periodic stream of Diracs (which is sparse in time-domain) are accessible. In its parametric form, this signal has a finite number of degrees of freedom per unit time. Based on the representation of this signal in FrFT domain, we derive conditions under which exact recovery of parameters of the signal is possible. Knowledge of these parameters leads to exact reconstruction of the original signal. |
| first_indexed | 2024-10-01T02:55:09Z |
| format | Journal Article |
| id | ntu-10356/92280 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:55:09Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | ntu-10356/922802020-03-07T14:02:36Z Sampling and reconstruction of sparse signals in fractional fourier domain Ayush Bhandari Pina Marziliano School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering Sampling theory for continuous time signals which have a bandlimited representation in fractional Fourier transform (FrFT) domain--a transformation which generalizes the conventional Fourier transform has blossomed in the recent past. The mechanistic principles behind Shannon's sampling theorem for fractional bandlimited (or fractional Fourier bandlimited) signals are the same as for the Fourier domain case i.e. sampling (and reconstruction) in FrFT domain can be seen as an orthogonal projection of a signal onto a subspace of fractional bandlimited signals. As neat as this extension of Shannon's framework is, it inherits the same fundamental limitation that is prevalent in the Fourier regime-what happens if the signals have singularities in the time domain (or the signal has a nonbandlimited spectrum)? In this paper, we propose a uniform sampling and reconstruction scheme for a class of signals which are nonbandlimited in FrFT sense. Specifically, we assume that samples of a smoothed version of a periodic stream of Diracs (which is sparse in time-domain) are accessible. In its parametric form, this signal has a finite number of degrees of freedom per unit time. Based on the representation of this signal in FrFT domain, we derive conditions under which exact recovery of parameters of the signal is possible. Knowledge of these parameters leads to exact reconstruction of the original signal. Published version 2010-12-23T02:40:52Z 2019-12-06T18:20:35Z 2010-12-23T02:40:52Z 2019-12-06T18:20:35Z 2010 2010 Journal Article Ayush, B., & Pina, M. (2010). Sampling and reconstruction of sparse signals in fractional fourier domain. IEEE Signal Processing Letters, 17(3), 221-224. 1070-9908 https://hdl.handle.net/10356/92280 http://hdl.handle.net/10220/6497 10.1109/LSP.2009.2035242 150965 en IEEE signal processing letters © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. http://www.ieee.org/portal/site This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. 4 p. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering Ayush Bhandari Pina Marziliano Sampling and reconstruction of sparse signals in fractional fourier domain |
| title | Sampling and reconstruction of sparse signals in fractional fourier domain |
| title_full | Sampling and reconstruction of sparse signals in fractional fourier domain |
| title_fullStr | Sampling and reconstruction of sparse signals in fractional fourier domain |
| title_full_unstemmed | Sampling and reconstruction of sparse signals in fractional fourier domain |
| title_short | Sampling and reconstruction of sparse signals in fractional fourier domain |
| title_sort | sampling and reconstruction of sparse signals in fractional fourier domain |
| topic | DRNTU::Engineering::Electrical and electronic engineering |
| url | https://hdl.handle.net/10356/92280 http://hdl.handle.net/10220/6497 |
| work_keys_str_mv | AT ayushbhandari samplingandreconstructionofsparsesignalsinfractionalfourierdomain AT pinamarziliano samplingandreconstructionofsparsesignalsinfractionalfourierdomain |