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.