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Pure Mathematics 2025
离散组合分数余弦变换
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Abstract:
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。
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.
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