Discrete Convolution Associated with Fractional Cosine and Sine Series  

作　　者：Xiuxiu Gao Qiang Feng Yinyin Mei Yi Xiang 

机构地区：[1]School of Mathematics and Computer Science,Yan’an University,Yan’an 716000,Shaanxi,China

出　　处：《Journal of Beijing Institute of Technology》2021年第3期305-310,共6页北京理工大学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.61861044,62001193,11961072 and 62041212);The Natural Science Foundation of Shaanxi Province(Nos.2020JM-547 and 2020JM-548);the Sci-ence Foundation of Yan’an University(Nos.YDY2017-05 and YDBK2018-36).

摘　　要：Fractional sine series(FRSS)and fractional cosine series(FRCS)are the discrete form of the fractional cosine transform(FRCT)and fractional sine transform(FRST).The recent stud-ies have shown that discrete convolution is widely used in optics,signal processing and applied mathematics.In this paper,firstly,the definitions of fractional sine series(FRSS)and fractional co-sine series(FRCS)are presented.Secondly,the discrete convolution operations and convolution theorems for fractional sine and cosine series are given.The relationship of two convolution opera-tions is presented.Lastly,the discrete Young’s type inequality is established.The proposed theory plays an important role in digital filtering and the solution of differential and integral equations.

关 键 词：fractional cosine series fractional sine series discrete convolution discrete Young’s in-equality 

分 类 号：O17[理学—数学]