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The components of the underwater target scattering waves alias together in time domain and frequency domain realistically. They are affected by the incident angle, and show great differences under different angles. It is necessary to build an analytical model of scattering waves under all-direction incident angles theoretically. The analytical expressions of geometrical scattering components changing with the incident angle in fractional Fourier transform domain are deduced in this paper. The all-direction model in optimal fractional Fourier transform domain of the scattering waves is built. Based on this, the geometrical feature of underwater target echo is provided. In addition, the relationships between the resolution and the bandwidth of transmitted signal, and between the calculation accuracy and the length of observational signal are given. By processing experimental data, it is indicated that the model in fractional Fourier transform domain is in accordance with the characteristics of underwater target. It can provide a theoretical basis for target recognition under unknown incident angle.
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Keywords:
- underwater target detection /
- geometrical scattering waves /
- fractional Fourier transform /
- resolution
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[2] Fan J 2001 Ph. D. Dissertation (Shanghai: Shanghai Jiaotong University) (in Chinese) [范军 2001 博士学位论文(上海: 上海交通大学)]
[3] Fan W, Zheng G Y, Fan J 2010 Acta Acustica 35 419 (in Chinese) [范威, 郑国垠, 范军 2010 声学学报 35 419]
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[6] Li L, Wen J H, Cai L, Zhao H G, Wen X S 2013 Chin. Phys. B 22 014301
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[9] Décultot D, Liétard R, Maze G 2010 J. Acoust. Soc. Am. 127 1328
[10] Chen Y F, Li G J, Wang Z S, Zhang M W, Jia B 2013 Acta Phys. Sin. 62 084302 (in Chinese) [陈云飞, 李桂娟, 王振山, 张明伟, 贾兵 2013 物理学报 62 084302]
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[12] Zheng G Y, Fan J, Tang W L 2010 Acta Acustica 35 31 (in Chinese) [郑国垠, 范军, 汤渭霖 2010 声学学报 35 31]
[13] Ou H H, Au W W L, Syrmos V L 2010 Oceans 2010 MTS/IEEE Seattle Seattle, USA, September 20-23, 2010 p1
[14] Anderson S D, Sabra K G, Zakharia M E, Sessarego J P 2012 J. Acoust. Soc. Am. 131 164
[15] Laaboubi M, Aassif E, Latif R, Dliou A, Maze G, Décultot D 2013 Aerosp. Sci. Technal. 27 216
[16] Tao R, Li X M, Li Y L, Wang Y 2009 IEEE Trans. Signal Process. 57 2852
[17] Deng B, Wang X, Tao R, Liu X Z 2012 Acta Armament. 33 764 (in Chinese) [邓兵, 王旭, 陶然, 刘贤忠 2012 兵工学报 33 764]
[18] Ozaktas H M, Kutay M A, Zalevsky Z 2001 The Fractional Fourier Transform with Applications in Optics and Signal Processing (New York: Wiley) pp1-5, 118-122
[19] Tao R, Deng B, Wang Y 2006 Sci. China: Inform. Sci. 49 1
[20] Sejdić E, Djurović I, Stanković L 2011 Signal Process. 91 1351
[21] Chen Y, Zhao H C, Chen S, Zhang S N 2014 Acta Phys. Sin. 63 118403 (in Chinese) [陈勇, 赵惠昌, 陈思, 张淑宁 2014 物理学报 63 118403]
[22] Tang W L 1994 Acta Acustica 19 92 (in Chinese) [汤渭霖 1994 声学学报 19 92]
[23] Tang W L, Chen D Z 1988 Acta Acustica 13 29 (in Chinese) [汤渭霖, 陈德智 1988 声学学报 13 29]
[24] Almeida L B 1994 IEEE Trans. Signal Process. 42 3084
[25] Liu F, Xu H F, Tao R, Wang Y 2012 Sci. China: Inform. Sci. 55 1301
[26] Ozaktas H M, Arikan O, Kutay M A, Bozdagi G 1996 IEEE Trans. Signal Process. 44 2141
[27] Xu H F, Liu F 2010 Proceedings of the 2010 IEEE International Conference on Information and Automation Harbin, China, June 20-23, 2010 p408
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[1] Li X K, Yang S E 2001 J. Harbin Eng. Univ. 22 25 (in Chinese) [李秀坤, 杨士莪 2001 哈尔滨工程大学学报 22 25]
[2] Fan J 2001 Ph. D. Dissertation (Shanghai: Shanghai Jiaotong University) (in Chinese) [范军 2001 博士学位论文(上海: 上海交通大学)]
[3] Fan W, Zheng G Y, Fan J 2010 Acta Acustica 35 419 (in Chinese) [范威, 郑国垠, 范军 2010 声学学报 35 419]
[4] Pan A, Fan J, Wang B 2013 J. Acoust. Soc. Am. 134 3452
[5] Pan A, Fan J, Zhuo L K 2013 Acta Phys. Sin. 62 024301 (in Chinese) [潘安, 范军, 卓琳凯 2013 物理学报 62 024301]
[6] Li L, Wen J H, Cai L, Zhao H G, Wen X S 2013 Chin. Phys. B 22 014301
[7] Williams K L, Kargl S G, Thorsos E I, Burnett D S, Lopes J L, Zampolli M, Marston P L 2010 J. Acoust. Soc. Am. 127 3356
[8] Waters Z J, Simpson H J, Sarkissian A, Dey S, Houston B H, Bucaro J A, Yoder T J 2012 J. Acoust. Soc. Am. 132 3076
[9] Décultot D, Liétard R, Maze G 2010 J. Acoust. Soc. Am. 127 1328
[10] Chen Y F, Li G J, Wang Z S, Zhang M W, Jia B 2013 Acta Phys. Sin. 62 084302 (in Chinese) [陈云飞, 李桂娟, 王振山, 张明伟, 贾兵 2013 物理学报 62 084302]
[11] Bucaro J A, Houston B H, Saniga M, Dragonette L R, Yoder T, Dey S, Kraus L, Carin L 2008 J. Acoust. Soc. Am. 123 738
[12] Zheng G Y, Fan J, Tang W L 2010 Acta Acustica 35 31 (in Chinese) [郑国垠, 范军, 汤渭霖 2010 声学学报 35 31]
[13] Ou H H, Au W W L, Syrmos V L 2010 Oceans 2010 MTS/IEEE Seattle Seattle, USA, September 20-23, 2010 p1
[14] Anderson S D, Sabra K G, Zakharia M E, Sessarego J P 2012 J. Acoust. Soc. Am. 131 164
[15] Laaboubi M, Aassif E, Latif R, Dliou A, Maze G, Décultot D 2013 Aerosp. Sci. Technal. 27 216
[16] Tao R, Li X M, Li Y L, Wang Y 2009 IEEE Trans. Signal Process. 57 2852
[17] Deng B, Wang X, Tao R, Liu X Z 2012 Acta Armament. 33 764 (in Chinese) [邓兵, 王旭, 陶然, 刘贤忠 2012 兵工学报 33 764]
[18] Ozaktas H M, Kutay M A, Zalevsky Z 2001 The Fractional Fourier Transform with Applications in Optics and Signal Processing (New York: Wiley) pp1-5, 118-122
[19] Tao R, Deng B, Wang Y 2006 Sci. China: Inform. Sci. 49 1
[20] Sejdić E, Djurović I, Stanković L 2011 Signal Process. 91 1351
[21] Chen Y, Zhao H C, Chen S, Zhang S N 2014 Acta Phys. Sin. 63 118403 (in Chinese) [陈勇, 赵惠昌, 陈思, 张淑宁 2014 物理学报 63 118403]
[22] Tang W L 1994 Acta Acustica 19 92 (in Chinese) [汤渭霖 1994 声学学报 19 92]
[23] Tang W L, Chen D Z 1988 Acta Acustica 13 29 (in Chinese) [汤渭霖, 陈德智 1988 声学学报 13 29]
[24] Almeida L B 1994 IEEE Trans. Signal Process. 42 3084
[25] Liu F, Xu H F, Tao R, Wang Y 2012 Sci. China: Inform. Sci. 55 1301
[26] Ozaktas H M, Arikan O, Kutay M A, Bozdagi G 1996 IEEE Trans. Signal Process. 44 2141
[27] Xu H F, Liu F 2010 Proceedings of the 2010 IEEE International Conference on Information and Automation Harbin, China, June 20-23, 2010 p408
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