Spatial Signal Analysis based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks

TL;DR

This paper introduces a wave-spectrum scaling method based on fractal theory for analyzing spatial signals in geographical systems, demonstrated through urban traffic networks in Chinese cities, and shows its potential for generalization to temporal signals.

Contribution

It presents a novel wave-spectrum scaling approach using fractal analysis for spatial signals, applicable to both self-similar and self-affine fractal signals in geographical contexts.

Findings

Urban traffic networks exhibit scaling law in wave-spectral density.

Spectral exponents can be converted to fractal dimensions.

Method can be generalized to temporal signal analysis.

Abstract

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.