%0 Journal Article
%T 离散组合分数余弦变换<br>Discrete Combined Fractional Cosine Transform
%A 胡蕴超
%A 茹艺
%J Pure Mathematics
%P 171-179
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.151020
%X 分数余弦变换是现代信号处理的常用工具&#65292;获得了广泛的发展。本文将以离散分数余弦变换(DFrCT)为研究对象&#65292;获得新的离散分数余弦变换&#8212;&#8212;离散组合分数余弦变换(DCFrCT)。信号的离散组合余弦变换(DCCT)是信号的正向离散余弦变换(DCT)和逆向离散余弦变换(IDCT)的线性组合。本文中引入的离散组合分数式余弦变换是DCCT到分数域的推广&#65292;可以看作是正向DFrCT和逆向DFrCT的线性组合。并在不同的分数阶下给出了信号的恢复方案&#65292;得到了在不同分数阶下的仿真结果。<br>Fractional cosine transform is a common tool in modern signal processing and has been widely developed. This paper takes discrete fractional cosine transform (DFrCT) as the research object and obtains a new discrete fractional cosine transform&#8212;discrete combined fractional cosine transform (DCFrCT). The discrete combined cosine transform (DCCT) of a signal is a linear combination of the forward discrete cosine transform (DCT) and the reverse discrete cosine transform (IDCT) of the signal. The discrete composite fractional cosine transform introduced in this paper is a generalization of DCCT to fractional domain and can be regarded as a linear combination of forward DFrCT and backward DFrCT. The signal recovery scheme is given in different fractional order, and the simulation results at different fractional orders are obtained.
%K 离散分数余弦变换&#65292
%K 离散组合分数余弦变换&#65292
%K 逆离散组合分数余弦变换<br>Discrete Fractional Cosine Transform
%K Discrete Combined Fractional Cosine Transform
%K Inverse Discrete Combined Fractional Cosine Transform
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106257