离散组合分数余弦变换
Discrete Combined Fractional Cosine Transform
摘要: 分数余弦变换是现代信号处理的常用工具，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，获得新的离散分数余弦变换——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，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，得到了在不同分数阶下的仿真结果。
Abstract: 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—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.
文章引用：胡蕴超, 茹艺. 离散组合分数余弦变换[J]. 理论数学, 2025, 15(1): 171-179. https://doi.org/10.12677/pm.2025.151020

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