Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks
Abstract
:1. Introduction
2. Models and Signals
2.1. Spatial Signals and Urban Density Models
2.2. Fourier Transform and Spectral Scaling Analysis
2.3. Wave-Spectral Scaling Relation
3. Empirical Analysis
3.1. Data and Methods
3.2. Results and Analysis
3.3. Cases of Power Spectral Scaling Analysis
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Type | Data | Object | Parameter | Complexity | Geographical Space |
---|---|---|---|---|---|
Temporal signal | Time series data | Dynamic evolution | Hurst exponent | Time lag | Phase space |
Spatial signal | Spatial data | Spatial distribution | Fractal dimension | Spatial dimension | Real space |
Hierarchical signal | Cross-sectional data | Rank-size distribution | Zipf exponent | Interaction | Order space |
Position | City | Coefficient F0 * | Spectral Exponent α | Goodness of Fit R2 | Fractal Dimension Df | Fractal Dimension Ds |
---|---|---|---|---|---|---|
North | Beijing | 0.0002092 | 0.9635 | 0.8543 | 1.9635 | 1.5365 |
Tianjin | 0.0005071 | 0.7567 | 0.9236 | 1.7567 | 1.7433 | |
South | Guangzhou | 0.0003429 | 0.9107 | 0.9152 | 1.9107 | 1.5893 |
Shenzhen | 0.0003437 | 0.9838 | 0.8525 | 1.9838 | 1.5162 | |
Central | Wuhan | 0.0002729 | 0.8884 | 0.9402 | 1.8884 | 1.6116 |
South-east | Nanjing | 0.0005069 | 0.7234 | 0.9104 | 1.7234 | 1.7766 |
Shanghai | 0.0005876 | 0.7707 | 0.8570 | 1.7707 | 1.7293 | |
Hangzhou | 0.0003653 | 0.8730 | 0.9291 | 1.8730 | 1.6270 | |
South-west | Chongqing | 0.0003146 | 0.8115 | 0.8455 | 1.8115 | 1.6885 |
Chengdu | 0.0003350 | 0.8697 | 0.8206 | 1.8697 | 1.6303 |
City | Spectral Analysis | R/S Analysis | ||||||
---|---|---|---|---|---|---|---|---|
P0 | β | R2 | Ds | Df | Coefficient | H | R2 | |
Baoding | 1532.2018 | 1.3649 | 0.5605 | 1.8176 | 1.6824 | 1.0111 | 0.5982 | 0.9373 |
Beijing | 25,950.7422 | 1.8009 | 0.8385 | 1.5995 | 1.9005 | 0.9317 | 0.6642 | 0.9542 |
Cangzhou | 1545.2501 | 1.3164 | 0.5322 | 1.8418 | 1.6582 | 0.9809 | 0.6280 | 0.9696 |
Chengde | 194.4615 | 1.4499 | 0.7281 | 1.7750 | 1.7250 | 0.9598 | 0.6366 | 0.9152 |
Handan | 1680.5985 | 1.4165 | 0.4976 | 1.7917 | 1.7083 | 1.2221 | 0.4628 | 0.7739 |
Hengshui | 295.9529 | 1.2741 | 0.6029 | 1.8629 | 1.6371 | 0.9621 | 0.6091 | 0.9344 |
Langfang | 2493.1480 | 1.4288 | 0.6164 | 1.7856 | 1.7144 | 1.0578 | 0.5842 | 0.9222 |
Qinhuangdao | 447.7705 | 1.6063 | 0.7843 | 1.6968 | 1.8032 | 1.1647 | 0.5625 | 0.9301 |
Shijiazhuang | 1866.2198 | 1.5853 | 0.6874 | 1.7074 | 1.7926 | 0.9727 | 0.6074 | 0.9366 |
Tangshan | 3534.1318 | 1.5370 | 0.7094 | 1.7315 | 1.7685 | 1.0489 | 0.5620 | 0.9332 |
Category | Type | Example | Method |
---|---|---|---|
Non-fractal signals | Stationary series | Random spatial processes | Conventional spatial statistics |
Trend series with characteristic scale | Exponential distribution of urban population density | Conventional mathematical methods and wave-spectrum scaling | |
Fractal signals | Self-similar series | Isotropic growing fractal networks | Wave-spectrum scaling based on correlation function |
Self-affine series | Anisotropic growing fractal networks | Wave-spectrum scaling relation |
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Chen, Y.; Long, Y. Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks. Appl. Sci. 2021, 11, 87. https://doi.org/10.3390/app11010087
Chen Y, Long Y. Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks. Applied Sciences. 2021; 11(1):87. https://doi.org/10.3390/app11010087
Chicago/Turabian StyleChen, Yanguang, and Yuqing Long. 2021. "Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks" Applied Sciences 11, no. 1: 87. https://doi.org/10.3390/app11010087
APA StyleChen, Y., & Long, Y. (2021). Spatial Signal Analysis Based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks. Applied Sciences, 11(1), 87. https://doi.org/10.3390/app11010087