多维解析信号分析和Hilbert变换在现代信号处理理论和工程应用中有着重要的意义.该文根据解析信号在广义频域内的能量分布,提出了二维信号的方向广义Hilbert变换、全向广义Hilbert变换以及单象广义Hilbert变换等定义,并证明了时域和分数阶Fourier域内它们之间的对应关系以及推导出类似于传统Hilbert变换中的性质.同时,给出了解析信号中具有重要意义的二维广义Bedrosian定理和相应的理论证明.%Hilbert transform (HT) plays an important role in signal processing. Prom the energy distributing of analytic signals in the FRFT domain and a few classical 2D elemen tary Hilbert transform, the definitions of half-planed Hilbert transform, cross-orthant Hilbert transform and single-orthant Hilbert transform are yielded. Meanwhile, the expressions and the mapping in the time domain and the transformed domain are discussed. Moreover, some important properties and conclusions are obtained as well. Finally, we define and derive 2D Bedrosian's principle in the FRFT domain, an important property of Hilbert transform.
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