-
Sampling and reconstruction of short pulses based on Gabor frames have been proved to be effective, which overcome the difficulties that finite rate of innovation (FRI) sampling is unable to reconstruct the pulse streams without the prior information of waveforms. However, the windows sequences of sampling scheme based on Gabor frames proposed at present show complicated structure and are hard to realize physically. The exponential reproducing windows are then introduced in this paper and the windows sequences can be simplified as a first-order analog Butterworth filter. At the same time, the compressed sensing (CS) measurement matrix is constructed for the recovery of Gabor coefficients. In order to satisfy the restricted isometry property (RIP) of the measurement matrices for perfect signal reconstruction, we select appropriate windows for support according to the energy accumulation property. A restricted condition is deduced for perfecting the signal reconstruction and the system robustness is analyzed. By numerical simulations the above analysis is verified. This novel scheme can be used to implement short pulses sampling and reconstruction in the field of instrumentation, condition monitoring, radar and the communication.
-
Keywords:
- Gabor frames /
- exponential reproducing windows /
- sub-Nyquist sampling /
- compressed sensing
[1] Fang S, Wu W C, Ying K, Guo H 2013 Acta Phys. Sin. 62 048702 (in Chinese) [方晟, 吴文川, 应葵, 郭华 2013 62 048702]
[2] Ning F L, He B J, Wei J 2013 Acta Phys. Sin. 62 174212 (in Chinese) [宁方立, 何碧静, 韦娟 2013 62 174212]
[3] Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩, 彭喜元 2014 63 030701]
[4] Omer Bar-Ilan, Eldar Y C 2014 IEEE Trans. Signal Processing 62 1796
[5] Herman M A, Strohmer T 2009 IEEE Trans. Signal Processing 57 2275
[6] Razzaque M A, Bleakley C, Dobson S 2013 ACM Transactions on Sensor Networks 10 5
[7] Mishali M, Eldar Y C, Dounaevsky O 2011 IET circuits, devices & systems 5 8
[8] Tropp J A, Laska J N, Duarte M F 2010 IEEE Trans. Inf. Theory 56 520
[9] Michaeli T, Eldar Y C 2012 Signal Processing, IEEE Transactions on. 60 1121
[10] Urigiien J A, Eldar Y C, Dragotti P L 2012 Compressed Sensing: Theory and Applications (Cambridge, U.K.: Cambridge Univ. Press) p148
[11] Matusiak E 2012 IEEE Ttransactions on Signal Processing 60 1134
[12] Kloos T, Stöckler J 2013 Journal of Approximation Theory 184 209
[13] Jeffrey D B, Michael C, David H, Yirong J 2013 IEEE Trans. Signal Processing 62 1694
[14] Xie Z P, Chen S C 2013 Journal of Computer Research and Development 49 580 (in Chinese) [谢志鹏, 陈松灿 2013 计算机研究与发展 49 580]
[15] Feichtinger H G 1981 Monatshefte fr Mathematik 92 269
[16] Mishali M, Eldar Y C 2009 Information Theory Workshop 2009.IEEE
[17] Daubenchies I 1992 Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics) p97
[18] Unser M, Blu T 2005 IEEE Trans. Signal Processing 53 1425
[19] Qu C W, He Y, Liu W H, Li N 2009 Frames Theory and Applications (Beijing: National Defense Industy Press) p152 (in Chinese) [曲长文, 何友, 刘卫华, 李楠 2009 框架理论及应用(北京: 国防工业出版社) 第152页]
[20] Tropp J A, Laska J N, Duarte M F, Romberg J K, Baraniuk R G 2010 IEEE Trans Inf. Theory 56 520
[21] Xu Z Q 2012 Scientia Sinica (Mathematica) 42 865 (in Chinese) [许志强 中国科学:数学 42 865]
[22] Haupt J, Nowak R 2010 Proc. 44th Annual Conf. on Information Sciences and Systems Princeton, NJ, March 2010
[23] Xu G W, Xu Z Q 2013 arXiv:1301.0373
[24] Rudelson M, Vershynin R 2008 Communications on Pure and Applied Mathematics 61 1025
-
[1] Fang S, Wu W C, Ying K, Guo H 2013 Acta Phys. Sin. 62 048702 (in Chinese) [方晟, 吴文川, 应葵, 郭华 2013 62 048702]
[2] Ning F L, He B J, Wei J 2013 Acta Phys. Sin. 62 174212 (in Chinese) [宁方立, 何碧静, 韦娟 2013 62 174212]
[3] Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩, 彭喜元 2014 63 030701]
[4] Omer Bar-Ilan, Eldar Y C 2014 IEEE Trans. Signal Processing 62 1796
[5] Herman M A, Strohmer T 2009 IEEE Trans. Signal Processing 57 2275
[6] Razzaque M A, Bleakley C, Dobson S 2013 ACM Transactions on Sensor Networks 10 5
[7] Mishali M, Eldar Y C, Dounaevsky O 2011 IET circuits, devices & systems 5 8
[8] Tropp J A, Laska J N, Duarte M F 2010 IEEE Trans. Inf. Theory 56 520
[9] Michaeli T, Eldar Y C 2012 Signal Processing, IEEE Transactions on. 60 1121
[10] Urigiien J A, Eldar Y C, Dragotti P L 2012 Compressed Sensing: Theory and Applications (Cambridge, U.K.: Cambridge Univ. Press) p148
[11] Matusiak E 2012 IEEE Ttransactions on Signal Processing 60 1134
[12] Kloos T, Stöckler J 2013 Journal of Approximation Theory 184 209
[13] Jeffrey D B, Michael C, David H, Yirong J 2013 IEEE Trans. Signal Processing 62 1694
[14] Xie Z P, Chen S C 2013 Journal of Computer Research and Development 49 580 (in Chinese) [谢志鹏, 陈松灿 2013 计算机研究与发展 49 580]
[15] Feichtinger H G 1981 Monatshefte fr Mathematik 92 269
[16] Mishali M, Eldar Y C 2009 Information Theory Workshop 2009.IEEE
[17] Daubenchies I 1992 Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics) p97
[18] Unser M, Blu T 2005 IEEE Trans. Signal Processing 53 1425
[19] Qu C W, He Y, Liu W H, Li N 2009 Frames Theory and Applications (Beijing: National Defense Industy Press) p152 (in Chinese) [曲长文, 何友, 刘卫华, 李楠 2009 框架理论及应用(北京: 国防工业出版社) 第152页]
[20] Tropp J A, Laska J N, Duarte M F, Romberg J K, Baraniuk R G 2010 IEEE Trans Inf. Theory 56 520
[21] Xu Z Q 2012 Scientia Sinica (Mathematica) 42 865 (in Chinese) [许志强 中国科学:数学 42 865]
[22] Haupt J, Nowak R 2010 Proc. 44th Annual Conf. on Information Sciences and Systems Princeton, NJ, March 2010
[23] Xu G W, Xu Z Q 2013 arXiv:1301.0373
[24] Rudelson M, Vershynin R 2008 Communications on Pure and Applied Mathematics 61 1025
Catalog
Metrics
- Abstract views: 6412
- PDF Downloads: 248
- Cited By: 0
下载:
