双指数积分法计算有限希尔伯特变换的研究

Study of finite Hilbert transformation via double exponential quadrature scheme

目的研究在单精度或双精度浮点数计算条件下,通过双指数变换（DE）计算有限希尔伯特变换（FHT）的有效性。方法为了避免浮点数溢出,我们由浮点的最大值作为输入参数,然后根据积分级数N计算出积分步长。结果如果把数组长度作为积分级数,采用单精度或双精度浮点数计算,双指数变换方法的FHT相对误差的数量级为10E-7～10E-5。结论双指数变换法可以被应用到某些领域进行快速FHT,如CT重建中。

Objective To study the effectiveness of finite Hilbert transformation （FHT） via double exponential （DE） quadrature scheme with single or double precision floating-point values. Methods To avoid floating point overflow, we calculate the input value according to the maximum of floating-point number and get corresponding integration step at a given level N. Results At level of the dimension of given data, the relative accuracy of FHT by DE method with single or double precision floating-point values is at the magnitude of 10E-7-10E-5. Conclusion DE quadrature scheme can be used for fast FHT in certain fields such as CT reconstruction.