论文标题
基于波光谱分形缩放的空间信号分析：城市街道网络的案例
Spatial Signal Analysis based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks
论文作者
论文摘要
长期以来，开发了许多方法来基于时间序列进行时间信号分析。但是，对于地理系统，空间信号分析与时间信号分析一样重要。非平稳的空间和时间过程与非线性相关，无法通过常规分析方法有效分析。分形理论为探索复杂性提供了强大的工具，对时空信号分析有帮助。本文致力于通过波光谱缩放来研究地理系统的空间信号。 10个中国城市的交通网络被视为积极研究的案例。快速傅立叶变换和最小二乘回归分析用于计算光谱指数。结果表明，所有这些城市交通网络的波光谱密度分布遵循缩放定律，光谱缩放指数可以转换为分形维度值。使用分形参数，我们可以对地理信号进行空间分析。分析过程可以推广到时间信号分析。波光谱缩放方法可以应用于地理世界中的自相似分形信号和自动分形信号。
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal processes are associated with nonlinearity, and cannot be effectively analyzed by conventional analytical approaches. Fractal theory provides a powerful tool for exploring complexity and is helpful for spatio-temporal signal analysis. This paper is devoted to researching spatial signals of geographical systems by means of wave-spectrum scaling. The traffic networks of 10 Chinese cities are taken as cases for positive studies. Fast Fourier transform and least squares regression analysis are employed to calculate spectral exponents. The results show that the wave-spectral density distribution of all these urban traffic networks follows scaling law, and the spectral scaling exponents can be converted to fractal dimension values. Using the fractal parameters, we can make spatial analyses for the geographical signals. The analytical process can be generalized to temporal signal analyses. The wave-spectrum scaling methods can be applied to both self-similar fractal signals and self-affine fractal signals in the geographical world.
