Discrete Convolution Associated with Fractional Cosine and Sine Series

• 作者: Xiuxiu Gao Qiang Feng Yinyin Mei Yi Xiang
• 来源期刊: 北京理工大学学报（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 305-310
• 页数: 6页
• 语种: 英文
• DOI: 10.15918/j.jbit1004-0579.2021.040

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.