基于快速傅立叶变换(FFT)的地形剖面线的数学表达研究

在数字地形分析中,地形剖面的分析方法不仅可以以线代面研究区域的地形起伏变化,还可很好地反映地形沿某一方向的地势起伏和坡度陡缓,其地形剖面线的数学表达更能为今后的数字地形分析提供坚实的数学基础.鉴于此,将信号分析中常用的傅立叶变换引入到地形剖面分析中,从信号分析的角度,把地形剖面线看成一维连续空间域信号,并对其傅里叶变换后的频谱进行研究分析.通过对地形剖面的频谱分析,可得到该地形剖面所包含的地形频率信息,进而实现地形剖面的数学表达.

Mathematics Expression of Terrain Profile Based on Fast Fourier Transform

Terrain profile analysis presents an effective tool for analyzing regional terrain changes by using lines rather than polygons,shows the steep(or flat) features of slope along certain directions,and provides a solid mathematics foundation for digital terrain analysis.We introduced the Fast Fourier Transform(FFT) which is commonly used in signal analysis into terrain profile analysis.Terrain profiles of a typical loess hilly-gully region were set up with high resolution DEM(digital elevation model) and were considered as one-dimensional continuous signals.The signals were converted to frequency spectrum through FFT and the spectrum diagrams resulted from FFT were analyzed.Through spectrum analysis,the terrain frequency information contained in the terrain profiles were obtained.Moreover,based on terrain analysis of eroded ditch in low resolution DEM,the terrain profiles were decomposed into components with different spatial frequencies.Subsequently the mathematics expression of terrain profiles were obtained.This research is an attempt to obtain more eroded terrain information from DEM and helps promote the combination of digital terrain analysis with soil erosion analysis.