摘要
哈特莱变换(HT)是一种与傅氏变换相似的积分变换,具有傅氏变换的大部分特性。利用与快速傅氏变换相同的结构可以构造快速哈特莱变换(FHT)。但是,与傅氏变换相比,哈特莱变换具有两个明显的优点:其一,正反变换是一致的;其二,它是一种实数变换。正因为如此,它的计算速度比傅氏变换快,因为实数运算所需的内存仅是复数的一半,所以在任何以傅氏变换为计算工具的数据处理过程中(如滤波、正演模拟和偏移等),用哈特莱变换代替傅氏变换,不仅速度快,而且节省内存。本文从傅氏变换的三角形式入手,推导了哈特莱变换的原始形式,阐述了哈特莱变换与傅氏变换和希尔伯特变换的关系。通过与傅氏变换的比较,证明了哈特莱变换的各种性质,并将这些性质推广到离散哈特莱变换和多维哈特莱变换。由于这些性质与傅氏变换的性质具有明显的相似性或相同性,所以很容易将目前普遍使用的傅氏变换程序转化为哈特莱变换程序,从而为更快地进行地震资料处理提供了一条捷径。
Gan Lideng.Hartley transform and its properties.OGP,1992,27(5):605～616 Hartley Transform(HT)is an integral transform similar to Fourier Trans- form(FT)and it inherits most FT properties.Fast Hartley Transform(FHT) can be achieved by using the structures similar to that in Fast Fourier Transform (FFT).However,HT has two advantages over FT:(1)the same forward and in- verse transforms,and(2)real number transform.As a result,HT is faster than FT because the internal storage needed in real number operation is half as mush as that in complex number operation.Hence,in many data processings with FT, such as filtering,forward modehng,migration and so on,HT results in faster operation and less internal storage than FT does. HT original formulae are derived from FT circular function expressions. The relationship between HT and FT or Hilbert transform is analysed in detail. HT properties are summed by comparing with FT,and they are extended to dis- crete HT and multidimensional HT.HT and FT have similar or same proper- ties,so that widely used FT program can be easy converted into HT program, resulting in faster seismic data processing.
出处
《石油地球物理勘探》
EI
CSCD
北大核心
1992年第5期605-616,共12页
Oil Geophysical Prospecting
关键词
傅氏变换
哈特莱变换
地震数据处理
Fourier transform
Hilbert transform
Hartley transform
property
seismic data processing
