论文标题
加权L2空间中有限的希尔伯特变换
Finite Hilbert Transform in Weighted L2 Spaces
论文作者
论文摘要
获得了加权希尔伯特变换的几种新特性。如果MU为零，则会得出两个类似Plancherel的方程和各向同性特性。对于MU是实际数字，得出了强制性，并构建了两个迭代序列以找到反转。所提出的迭代序列适用于带有| ETA | <pi/4的纯假想常数mu = i*eta的情况。对于MU = 0.0和3.0，我们使用有限的Hilbert Transform的Chebyshev系列表示，介绍了计算机模拟结果。本文中的结果对几种成像应用中的半扫描很有用。
Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are constructed to find the inversion. The proposed iterative sequences are applicable to the case of pure imaginary constant mu=i*eta with |eta|<pi/4 . For mu=0.0 and 3.0 , we present the computer simulation results by using the Chebyshev series representation of finite Hilbert transform. The results in this paper are useful to the half scan in several imaging applications.
