WANG Xiaobo, ZHANG Qiliang, ZHOU You, QIAN Jing, ZOU Hongxing. Linear Canonical Transform Related Operators and Their Applications to Signal Analysis—— Part I: Fundamentals[J]. Chinese Journal of Electronics, 2015, 24(1): 102-109.
Citation: WANG Xiaobo, ZHANG Qiliang, ZHOU You, QIAN Jing, ZOU Hongxing. Linear Canonical Transform Related Operators and Their Applications to Signal Analysis—— Part I: Fundamentals[J]. Chinese Journal of Electronics, 2015, 24(1): 102-109.

Linear Canonical Transform Related Operators and Their Applications to Signal Analysis—— Part I: Fundamentals

Funds:  This work is supported by the National Natural Science Foundation of China (No.11301024, No.61071222).
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  • Corresponding author: ZOU Hongxing was born in 1966 in Jiangsu Province. He currently is a professor at the Department of Automation, Tsinghua University, Beijing, China. His research interests include signal processing, pattern recognition and matrix factorization. (Hongxing_Zou@tsinghua.edu.cn)
  • Received Date: 2014-04-01
  • Rev Recd Date: 2014-06-01
  • Publish Date: 2015-01-10
  • In recent years, the Linear canonical transform (LCT) has been recognized as a powerful tool in signal processing scenarios and optics. In this two-part paper, the issue of unitary and Hermitian operators and their duality concept associated with LCT are addressed. In Part I, based on the proposed operators, three LCT-related topics are derived. Firstly, the definitions of convolution and correlation operations in LCT domain are constructed. Secondly, a new transform which is named as Linear canonical mellin transform (LCMT) is introduced and then convolution and correlation operations in LCMT domain are given. Thirdly, the so-called joint canonical distributions which satisfy the canonical transform marginal are given. Part II concerns two applications of the theory derived in Part I for signal analysis.
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