# Analysing Interlinked Frequency Dynamics of the Urban Acoustic Environment

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Recording Methods

#### 2.2. Land Use Types

## 3. Materials and Methods

#### 3.1. Pre-Processing

_{24}). Briefly, the AAP

_{24}dataset comprises 416,797 3-min recordings from 23 LUTs.

#### 3.1.1. Plausibility Check

#### 3.1.2. Calculation of Power Spectra

#### 3.1.3. De-Noising and Outlier Removal

#### 3.2. Median Power Spectrum

#### 3.3. Normalised Spectrograms

#### 3.4. Correlation Matrices

^{2}as a measure of the proportion of explained variance between two frequencies. Here, high values of R

^{2}indicate a strong relationship between frequencies, which is due to sound sources that occur simultaneously or closely subsequent in time and occupy multiple frequency bins. As occurrences of most sound sources are independent from each other (e.g., dogs barking, cars passing by, etc.), this method yields the opportunity to characterise different LUTs in regard to how their sound sources differ in prevalence from each other. For a more intuitive understanding of how FCMs work for specific sound sources, we show nine common sound source examples and their corresponding FCMs in Appendix A (Figure A2). Still, it is important to note that we correlate power spectra of 3-min recordings, therefore a high R

^{2}between a pair of frequencies implies either the presence of a single sound source that occupies these two frequencies over several recordings (i.e., h) or multiple distinct sound sources that are linked in their occurrence over this time scale (3-min) (e.g., wind and rustling leaves). For this reason, and because the urban acoustic environment is always a mixture of a variety of sounds, FCMs are not intended to identify sound sources, but rather are used as a tool to characterise the particular LUT through its overall frequency dynamics over time.

^{2}values for each LUT, allowing us to analyse the distribution of correlation coefficients and therefore to identify multimodal distributions. Multimodal distributions can be seen as a mixture of multiple underlying distributions, potentially representing different groups [51]. In our case, a multimodal distribution results from the prevalence of different R

^{2}values (i.e., correlated frequency bins) and may be an indicator for the diversity of sound sources.

## 4. Results

#### 4.1. Median Power Spectrum

#### 4.2. Normalised Spectrograms

#### 4.3. Correlation Matrices

^{2}= 0.5, indicating somewhat prominent additional sound interrelations, the overwhelming majority of values is close to 1. In contrast, LUTs for Figure 5d–i show clear differences in their FCMs and histograms. The striking commonality of these LUTs are the distinct square patterns. Here, frequencies > ~9.5 kHz consistently form a community. This finding is not obvious when looking only at the spectrograms from Figure 4. From there, one might be misled into assuming that this frequency range is connected to lower frequencies (<2.5 kHz) as in Figure 4b or Figure 4c. However, from correlation matrices we can derive that there are independent sound sources (in)active in this range. Only Figure 5d,e,h show higher correlations between >9.5 kHz and <700 Hz that can also be seen in the traffic-related LUTs. Although Figure 5d,i also show moderate-to-high correlations between >9.5 kHz and lower Hz (1–1.5 kHz), the latter range is different from the one observed in the “Main/Residential Street”.

^{2}-value distribution, but they differ in magnitude. All six LUTs show a multimodal distribution of R

^{2}values, most of them with a second peak at around R

^{2}= 0.4. While “Residential Area”, “Play- or Sportsground” and “Green Space” seem to be very similar, “Small Garden near house” shows a prevalence of R

^{2}values close to 0.3 similar to those close to 1 (note that the diagonal ones that come from correlating the frequency bin with itself were removed).

## 5. Discussion

^{2}-distribution consequently yielded valuable information on the complexity of different urban AEs. Our results give evidence that correlations between frequency powers are a promising approach to describe the urban acoustic environment, as they not only map the frequency spectrum, but also consider the temporal dimension at the same time.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Percentage of land use area (as defined by Ruhr Regional Association [41]) in a 50 m radius buffer around each recording station. Depicted are the ten largest land use types, which in total occupy more than 94% of the 50 m buffer area.

**Figure A2.**Sound source examples and their corresponding correlation matrices. A spectrogram was calculated for the corresponding audio recording. Then, power of all frequency bins were correlated over time for the period in which the sound source occurred. The Z-axis represents the Pearson correlation coefficient. The insert shows the distribution of all correlation values of the respective correlation matrix.

## References

- Van Kempen, E.; Casas, M.; Pershagen, G.; Foraster, M. WHO Environmental Noise Guidelines for the European Region: A systematic review on environmental noise and cardiovascular and metabolic effects: A summary. Int. J. Environ. Res. Public Health
**2018**, 15, 379. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Babisch, W.; Beule, B.; Schust, M.; Kersten, N.; Ising, H. Traffic noise and risk of myocardial infarction. Epidemiology
**2005**, 16, 33–40. [Google Scholar] [CrossRef] - Barregard, L.; Bonde, E.; Ohrstrom, E. Risk of hypertension from exposure to road traffic noise in a population-based sample. Occup. Environ. Med.
**2009**, 66, 410–415. [Google Scholar] [CrossRef] [PubMed] - Fuks, K.; Moebus, S.; Hertel, S.; Viehmann, A.; Nonnemacher, M.; Dragano, N.; Mohlenkamp, S.; Jakobs, H.; Kessler, C.; Erbel, R.; et al. Long-term urban particulate air pollution, traffic noise, and arterial blood pressure. Environ. Health Perspect.
**2011**, 119, 1706–1711. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kälsch, H.; Hennig, F.; Moebus, S.; Möhlenkamp, S.; Dragano, N.; Jakobs, H.; Memmesheimer, M.; Erbel, R.; Jöckel, K.-H.; Hoffmann, B. Are air pollution and traffic noise independently associated with atherosclerosis: The Heinz Nixdorf Recall Study. Eur. Heart J.
**2014**, 35, 853–860. [Google Scholar] [CrossRef] [Green Version] - Orban, E.; McDonald, K.; Sutcliffe, R.; Hoffmann, B.; Fuks, K.B.; Dragano, N.; Viehmann, A.; Erbel, R.; Jöckel, K.-H.; Pundt, N. Residential road traffic noise and high depressive symptoms after five years of follow-up: Results from the Heinz Nixdorf recall study. Environ. Health Perspect.
**2016**, 124, 578–585. [Google Scholar] [CrossRef] [Green Version] - Selander, J.; Nilsson, M.E.; Bluhm, G.; Rosenlund, M.; Lindqvist, M.; Nise, G.; Pershagen, G. Long-term exposure to road traffic noise and myocardial infarction. Epidemiology
**2009**, 20, 272–279. [Google Scholar] [CrossRef] - Sørensen, M.; Andersen, Z.J.; Nordsborg, R.B.; Becker, T.; Tjønneland, A.; Overvad, K.; Raaschou-Nielsen, O. Long-Term exposure to road traffic noise and incident diabetes: A cohort study. Environ. Health Perspect.
**2013**, 121, 217–222. [Google Scholar] [CrossRef] [Green Version] - Sørensen, M.; Hvidberg, M.; Andersen, Z.J.; Nordsborg, R.B.; Lillelund, K.G.; Jakobsen, J.; Tjønneland, A.; Overvad, K.; Raaschou-Nielsen, O. Road traffic noise and stroke: A prospective cohort study. Eur. Heart J.
**2011**, 32, 737–744. [Google Scholar] [CrossRef] [Green Version] - Kang, J.; Aletta, F.; Gjestland, T.T.; Brown, L.A.; Botteldooren, D.; Schulte-Fortkamp, B.; Lercher, P.; van Kamp, I.; Genuit, K.; Fiebig, A. Ten questions on the soundscapes of the built environment. Build. Environ.
**2016**, 108, 284–294. [Google Scholar] [CrossRef] - Araújo Alves, J.; Neto Paiva, F.; Torres Silva, L.; Remoaldo, P. Low-Frequency Noise and Its Main Effects on Human Health—A Review of the Literature between 2016 and 2019. Appl. Sci.
**2020**, 10, 5205. [Google Scholar] [CrossRef] - Baliatsas, C.; van Kamp, I.; van Poll, R.; Yzermans, J. Health effects from low-frequency noise and infrasound in the general population: Is it time to listen? A systematic review of observational studies. Sci. Total Environ.
**2016**, 557, 163–169. [Google Scholar] [CrossRef] [PubMed] [Green Version] - van Kamp, I.; van den Berg, F. Health Effects Related to Wind Turbine Sound, Including Low-Frequency Sound and Infrasound. Acoust. Aust.
**2018**, 46, 31–57. [Google Scholar] [CrossRef] [Green Version] - Aletta, F.; Oberman, T.; Kang, J. Associations between positive health-related effects and soundscapes perceptual constructs: A systematic review. Int. J. Environ. Res. Public Health
**2018**, 15, 2392. [Google Scholar] [CrossRef] [Green Version] - Alvarsson, J.J.; Wiens, S.; Nilsson, M.E. Stress Recovery during Exposure to Nature Sound and Environmental Noise. Int. J. Environ. Res. Public Health
**2010**, 7, 1036–1046. [Google Scholar] [CrossRef] - Medvedev, O.; Shepherd, D.; Hautus, M.J. The restorative potential of soundscapes: A physiological investigation. Appl. Acoust.
**2015**, 96, 20–26. [Google Scholar] [CrossRef] - Öhrström, E.; Skånberg, A.; Svensson, H.; Gidlöf-Gunnarsson, A. Effects of road traffic noise and the benefit of access to quietness. J. Sound Vib.
**2006**, 295, 40–59. [Google Scholar] [CrossRef] - Jiang, L.; Bristow, A.; Kang, J.; Aletta, F.; Thomas, R.; Notley, H.; Thomas, A.; Nellthorp, J. Ten questions concerning soundscape valuation. Build. Environ.
**2022**, 219, 109231. [Google Scholar] [CrossRef] - Wang, V.-S.; Lo, E.-W.; Liang, C.-H.; Chao, K.-P.; Bao, B.-Y.; Chang, T.-Y. Temporal and spatial variations in road traffic noise for different frequency components in metropolitan Taichung, Taiwan. Environ. Pollut.
**2016**, 219, 174–181. [Google Scholar] [CrossRef] - Farina, A. Soundscape Ecology: Principles, Patterns, Methods and Applications; Springer: Dordrecht, The Netherlands, 2013. [Google Scholar]
- Kasten, E.P.; Gage, S.H.; Fox, J.; Joo, W. The remote environmental assessment laboratory’s acoustic library: An archive for studying soundscape ecology. Ecol. Inform.
**2012**, 12, 50–67. [Google Scholar] [CrossRef] - Krause, B.; Farina, A. Using ecoacoustic methods to survey the impacts of climate change on biodiversity. Biol. Conserv.
**2016**, 195, 245–254. [Google Scholar] [CrossRef] - Pijanowski, B.C.; Farina, A.; Gage, S.H.; Dumyahn, S.L.; Krause, B.L. What is soundscape ecology? An introduction and overview of an emerging new science. Landsc. Ecol.
**2011**, 26, 1213–1232. [Google Scholar] [CrossRef] - Sueur, J. Sound Analysis and Synthesis with R; Springer: Culemborg, The Netherlands, 2018. [Google Scholar]
- Sueur, J.; Farina, A. Ecoacoustics: The ecological investigation and interpretation of environmental sound. Biosemiotics
**2015**, 8, 493–502. [Google Scholar] [CrossRef] - Bradfer-Lawrence, T.; Gardner, N.; Bunnefeld, L.; Bunnefeld, N.; Willis, S.G.; Dent, D.H. Guidelines for the use of acoustic indices in environmental research. Methods Ecol. Evol.
**2019**, 10, 1796–1807. [Google Scholar] [CrossRef] - Fairbrass, A.J.; Rennert, P.; Williams, C.; Titheridge, H.; Jones, K.E. Biases of acoustic indices measuring biodiversity in urban areas. Ecol. Indic.
**2017**, 83, 169–177. [Google Scholar] [CrossRef] - Haselhoff, T.; Hornberg, J.; Fischer, J.L.; Lawrence, B.T.; Ahmed, S.; Gruehn, D.; Moebus, S. The acoustic environment before and during the SARS-CoV-2 lockdown in a major German city as measured by ecoacoustic indices. J. Acoust. Soc. Am.
**2022**, 152, 1192–1200. [Google Scholar] [CrossRef] [PubMed] - Gibb, R.; Browning, E.; Glover-Kapfer, P.; Jones, K.E. Emerging opportunities and challenges for passive acoustics in ecological assessment and monitoring. Methods Ecol. Evol.
**2019**, 10, 169–185. [Google Scholar] [CrossRef] [Green Version] - Haselhoff, T.; Lawrence, B.; Hornberg, J.; Ahmed, S.; Sutcliffe, R.; Gruehn, D.; Moebus, S. The acoustic quality and health in urban environments (SALVE) project: Study design, rationale and methodology. Appl. Acoust.
**2022**, 188, 108538. [Google Scholar] [CrossRef] - Gage, S.H.; Towsey, M.; Kasten, E.P. Analytical Methods in Ecoacoustics. Ecoacoustics.
**2017**, 16, 273–296. [Google Scholar] [CrossRef] - Achard, S.; Salvador, R.; Whitcher, B.; Suckling, J.; Bullmore, E. A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs. J. Neurosci.
**2006**, 26, 63–72. [Google Scholar] [CrossRef] [Green Version] - Donges, J.F.; Zou, Y.; Marwan, N.; Kurths, J. Complex networks in climate dynamics. Eur. Phys. J. Spec. Top.
**2009**, 174, 157–179. [Google Scholar] [CrossRef] [Green Version] - Miksis-Olds, J.L.; Nichols, S.M. Is low frequency ocean sound increasing globally? J. Acoust. Soc. Am.
**2016**, 139, 501–511. [Google Scholar] [CrossRef] [Green Version] - Nichols, S.M.; Bradley, D.L. Use of noise correlation matrices to interpret ocean ambient noise. J. Acoust. Soc. Am.
**2019**, 145, 2337–2349. [Google Scholar] [CrossRef] [PubMed] - Asensio, C.; Pavón, I.; de Arcas, G. Changes in noise levels in the city of Madrid during COVID-19 lockdown in 2020. J. Acoust. Soc. Am.
**2020**, 148, 1748–1755. [Google Scholar] [CrossRef] - Hornberg, J.; Haselhoff, T.; Lawrence, B.T.; Fischer, J.L.; Ahmed, S.; Gruehn, D.; Moebus, S. Impact of the COVID-19 Lockdown Measures on Noise Levels in Urban Areas—A Pre/during Comparison of Long-Term Sound Pressure Measurements in the Ruhr Area, Germany. Int. J. Environ. Res. Public Health
**2021**, 18, 4653. [Google Scholar] [CrossRef] [PubMed] - Basu, B.; Murphy, E.; Molter, A.; Sarkar Basu, A.; Sannigrahi, S.; Belmonte, M.; Pilla, F. Investigating changes in noise pollution due to the COVID-19 lockdown: The case of Dublin, Ireland. Sustain. Cities Soc.
**2021**, 65, 102597. [Google Scholar] [CrossRef] - Acoustics, W. Song Meter SM4 Acoustic Recorder. Available online: https://www.wildlifeacoustics.com/products/song-meter-sm4 (accessed on 10 November 2022).
- ISO/TS 12913-2:2018; Acoustics—Soundscape—Part 2: Data Collection and Reporting Requirements. ISO: Geneva, Switzerland, 2014.
- Regionalverband Ruhr. Flächennutzungskartierung. Daten Für Die Stadt- Und Regionalplanung. Available online: https://www.rvr.ruhr/daten-digitales/geodaten/flaechennutzungskartierung/ (accessed on 10 November 2022).
- Sueur, J.; Aubin, T.; Simonis, C. Seewave, a free modular tool for sound analysis and synthesis. Bioacoustics
**2008**, 18, 213–226. [Google Scholar] [CrossRef] - Villanueva-Rivera, L.J.; Pijanowski, B.C.; Villanueva-Rivera, M.L.J. Package ‘soundecology’. R Package Version
**2018**, 1, 3. [Google Scholar] - Israel, G.D. Determining Sample Size; University of Florida: Gainesville, FL, USA, 1992. [Google Scholar]
- Cooley, J.W.; Tukey, J.W. An Algorithm for the Machine Calculation of Complex Fourier Series. Math. Comput.
**1965**, 19, 297–301. [Google Scholar] [CrossRef] - Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] [Green Version] - Hotelling, H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol.
**1933**, 24, 417. [Google Scholar] [CrossRef] - Abdi, H.; Williams, L.J. Principal component analysis. Wiley Interdiscip. Rev. Comput. Stat.
**2010**, 2, 433–459. [Google Scholar] [CrossRef] - Wilcox, R.R. Introduction to Robust Estimation and Hypothesis Testing, 2nd ed.; Academic Press: San Diego, CA, USA, 2011. [Google Scholar]
- Benesty, J.; Chen, J.; Huang, Y.; Cohen, I. Pearson correlation coefficient. In Noise Reduction in Speech Processing; Springer: Berlin/Heidelberg, Germany, 2009; pp. 1–4. [Google Scholar]
- McLachlan, G.J.; Lee, S.X.; Rathnayake, S.I. Finite mixture models. Annu. Rev. Stat. Its Appl.
**2019**, 6, 355–378. [Google Scholar] [CrossRef] - Boelman, N.T.; Asner, G.P.; Hart, P.J.; Martin, R.E. Multi-Trophic Invasion Resistance in Hawaii: Bioacoustics, Field Surveys, and Airborne Remote Sensing. Ecol. Appl.
**2007**, 17, 2137–2144. [Google Scholar] [CrossRef] [PubMed] - Ma, X.; Wu, Z.; Jia, J.; Xu, M.; Meng, H.; Cai, L. Emotion Recognition from Variable-Length Speech Segments Using Deep Learning on Spectrograms. In Proceedings of the Interspeech, Hyderabad, India, 2–3 September 2018; pp. 3683–3687. [Google Scholar]
- Towsey, M.W.; Truskinger, A.M.; Roe, P. The Navigation and Visualisation of Environmental Audio Using Zooming Spectrograms. In Proceedings of the 2015 IEEE International Conference on Data Mining Workshop (ICDMW), Atlantic City, NJ, USA, 14–17 November 2015; pp. 788–797. [Google Scholar]

**Figure 1.**Pictures and classification of the urban environment around all nine recording devices. The number in brackets is the number of 3-min recordings per site. In total, 130,017 recordings were used for this work.

**Figure 2.**Spectral entropy (

**a**) and intra-bin variance (

**b**) for 50 different bin counts, averaged over 16,000 recordings (black line). The grey line displays the relative change of subsequent values to each other, and the blue shaded area indicates where this value is below 10% of its maximum change.

**Figure 3.**Log-scale frequency spectrum for all recordings, grouped by land use type (

**a**–

**i**). The black line represents the median of all recordings, and the blue area the range between the 5% and 95% quantile.

**Figure 4.**Normalised Spectrograms for all LUTs (

**a**–

**i**). A mean power spectrum was calculated for all recordings per date/device. Subsequently, for each frequency bin (i.e., time series), the power was normalised so that the values correspond to the relative power of the frequency to itself. Thus, one is the maximum measured power and zero is the minimum measured power of the respective frequency bin. Black columns represent maintenance days, during which no recordings were made.

**Figure 5.**Frequency correlation matrices (FCMs) for all recordings over time, grouped by LUT (

**a**–

**i**). Here, the power spectra of each recording were correlated over time to identify temporally related frequency patterns. The Z-axis represents the squared Pearson correlation coefficient R

^{2}. The insert shows the distribution of all R

^{2}values of the respective correlation matrix (diagonal 1s caused by correlating the frequency bin with itself were removed for this purpose).

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## Share and Cite

**MDPI and ACS Style**

Haselhoff, T.; Braun, T.; Hornberg, J.; Lawrence, B.T.; Ahmed, S.; Gruehn, D.; Moebus, S.
Analysing Interlinked Frequency Dynamics of the Urban Acoustic Environment. *Int. J. Environ. Res. Public Health* **2022**, *19*, 15014.
https://doi.org/10.3390/ijerph192215014

**AMA Style**

Haselhoff T, Braun T, Hornberg J, Lawrence BT, Ahmed S, Gruehn D, Moebus S.
Analysing Interlinked Frequency Dynamics of the Urban Acoustic Environment. *International Journal of Environmental Research and Public Health*. 2022; 19(22):15014.
https://doi.org/10.3390/ijerph192215014

**Chicago/Turabian Style**

Haselhoff, Timo, Tobias Braun, Jonas Hornberg, Bryce T. Lawrence, Salman Ahmed, Dietwald Gruehn, and Susanne Moebus.
2022. "Analysing Interlinked Frequency Dynamics of the Urban Acoustic Environment" *International Journal of Environmental Research and Public Health* 19, no. 22: 15014.
https://doi.org/10.3390/ijerph192215014