Volume 32 Issue 3
May  2023
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MEI Yinyin, FENG Qiang, GAO Xiuxiu, et al., “Convolution Theorem Associated with the QWFRFT,” Chinese Journal of Electronics, vol. 32, no. 3, pp. 485-492, 2023, doi: 10.23919/cje.2021.00.225
Citation: MEI Yinyin, FENG Qiang, GAO Xiuxiu, et al., “Convolution Theorem Associated with the QWFRFT,” Chinese Journal of Electronics, vol. 32, no. 3, pp. 485-492, 2023, doi: 10.23919/cje.2021.00.225

Convolution Theorem Associated with the QWFRFT

doi: 10.23919/cje.2021.00.225
Funds:  This work was supported by the National Natural Science Foundation of China (61861044, 11961072, 62001193 ), the Natural Science Foundation of Shaanxi Province (2022JM-400, 2020JM-547), and the Graduate Education Innovation Program of Yan’an University (YCX2021047)
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  • Author Bio:

    Yinyin MEI was born in Shaanxi Province, China, in 1995. She received the B.S. degree from Yan’an University. She is an M.S. candidate in the School of Mathematics and Computer Science of Yan’an University. Her research interests include fractional convolution theory and fast algorithm. (Email: 2392471433@qq.com)

    Qiang FENG (corresponding author) was born in Shaanxi Province, China, in 1975. He received the B.S. and M.S. degrees from Yan’an University, Shaanxi, China, in 1998 and 2006, respectively, and the Ph.D. degree from Beijing Institute of Technology, Beijing, China, in 2018. He is currently an Associate Professor with the School of Mathematics and Computer Science in Yan’an University. His research interests include fractional Fourier transform, linear canonical transform, and mathematical methods in signal processing. (Email: yadxfq@yau.edu.cn)

  • Received Date: 2021-07-06
  • Accepted Date: 2022-08-14
  • Available Online: 2022-04-14
  • Publish Date: 2023-05-05
  • The quaternion windowed fractional Fourier transform (QWFRFT) is a generalized form of the quaternion fractional Fourier transform (QFRFT), it plays a crucial role in signal processing for the analysis of multidimensional signals. In this paper, we first give the definition of the two-sided QWFRFT and some fundamental properties. Then, the quaternion convolution is proposed, and the relation between the quaternion convolution and the classical convolution is also given. Based on the quaternion convolution of the QWFRFT, relevant convolution theorems for the QWFRFT are studied. Moreover, the fast algorithm for QWFRFT is discussed. Finally, the complexity of QWFRFT and the quaternion windowed fractional convolution are given.
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