Filtering, Visualizing, and Interpreting Spatial Time Series Data

Filtering, Visualizing, and Interpreting Spatial Time Series Data

Spatial time series (consecutive measurements across space and time) are often difficult to interpret, especially when there are many overlapping signals. These types of datasets can be found in many contexts, typically from sensors that quantify a series of measurements as a digital signal. 

For example, one source of dense spatial time series data is measurements from Distributed Acoustic Sensing (DAS). DAS is a form of Distributed Fiber Optic Sensing (DFOS) that measures sound/vibration signals along an optical fiber. This technology transforms fiber optic cables (typically used for telecommunications) into long sensors that act as an array of microphones every meter along the fiber [1][2][3]. 

We’ll look at an example of about a minute of DAS measurements of a pedestrian running along an 88-meter section of fiber optic cable under a road. In this case, the DAS measurements captured sound/vibration signals every meter along the road at a 10,000 Hz sampling rate. The resulting data consists of a large spatial time series: a 2D array of location (columns) vs. time (rows), with the quantified sound/vibration signal in each array cell location.

Figure 1. DAS measurements along an 88-meter section of roadway.

These DAS measurements of strain (in units of microstrain µε) can be visualized across space (location along the fiber in meters) and time (in seconds) in a waterfall plot. When we look at a waterfall plot of the raw unfiltered DAS measurements, we can interpret that our measurements have captured: 

• Lower frequency signals at different locations along the fiber that appear as long horizontal streaks across the plot.

• Higher frequency signals at specific locations and times that appear as small spots that form a triangle shape across the plot.

Figure 2. Unfiltered DAS strain measurements along a fiber over time (no filter).

Although we can approximately see our signal of interest in the form of a triangle shape from the pedestrian running up and down the road, the signals are obscured and rather unclear. Can we somehow process this data to isolate the signals of interest? Let’s walk through how this data can be elegantly filtered to isolate the signals of interest.

Filtering and Visualizing the Spatial Time Series Data

A typical method used to process this type of data involves isolating different frequency components of the time series, then filtering them depending on which components we want to keep or remove. For our data (50 - 60 seconds of measurements captured at a 10,000 Hz measurement rate), we can inspect signals at four example frequency bands:

Table 1. Bandpass filter frequency ranges 

We will use a Butterworth bandpass filter to filter our data. In theory, we expect the Butterworth filter will keep frequency components of our signal inside our desired frequency passband, and remove the others. Applying the bandpass filter for several neighboring passbands will help us isolate and compare different frequency components of our raw unfiltered data.

Figure 3. Butterworth bandpass filter frequency response across four frequency bands.

When we apply the 0.01 - 0.1 Hz bandpass filter, we see that the low-frequency components that we initially saw as long horizontal streaks in the raw data have been isolated. These signals can be interpreted as low-frequency drift in the measurement signal.

Figure 4. Filtered DAS strain measurements along a fiber over time (0.01 - 0.1 Hz bandpass filter).

When we apply the 0.1 - 1 Hz bandpass filter, we see some lower frequency components emerge as shorter streaks concentrated along the triangle path along the fiber. Although these signals seem to more closely capture the moving signal source of the pedestrian running up and down the road, it seems there are still some low-frequency drift streaks in the visualization.

Figure 5. Filtered DAS strain measurements along a fiber over time (0.1 - 1 Hz bandpass filter).

When we apply the 1 - 10 Hz bandpass filter, we now see the higher frequency components emerge as small spots along the triangle path along the fiber. These signals reveal that a moving signal source traveled up and down the fiber over about 50 seconds.

Figure 6. Filtered DAS strain measurements along a fiber over time (1 - 10 Hz bandpass filter).

When we apply the 10 - 100 Hz bandpass filter, we now see some higher frequency components along the triangle path along the fiber seemingly fade away. These less visible signals reveal that although the moving signal source generated some 10 - 100 Hz signals, they are much weaker than the 1 - 10 Hz signals.

Figure 7. Filtered DAS strain measurements along a fiber over time (10 - 100 Hz bandpass filter).

Interpreting the Spatial Time Series Data

After visualizing and comparing the DAS strain waterfall plots of the spatial time series data of the bandpass filtered strain signals, we can conclude that our signals of interest were in the 1 - 10 Hz bandpass filtered data. The output data from this filter revealed that our moving signal source moved along the fiber and emitted characteristic vibrations. As it turns out, these signals were emitted by a pedestrian running along the road!

Figure 8. Pedestrian footstep signals in filtered DAS strain measurements (0.1 - 10 Hz bandpass filter).

In conclusion, although spatial time series data may often seem noisy and difficult to interpret, filtering and visualizing the data always helps.

References

1. Soga, K., & Luo, L. (2018). Distributed fiber optics sensors for civil engineering infrastructure sensing. Journal of Structural Integrity and Maintenance, 3(1), 1–21. https://doi.org/10.1080/24705314.2018.1426138

2. Hubbard, P. G., Ou, R., Xu, T., & Soga, K. (2022). Road deformation monitoring and event detection using asphalt-embedded distributed acoustic sensing (DAS). Structural Control and Health Monitoring, 29(11), e3067.https://doi.org/10.1002/stc.3067

3. Saw, J., Apoji, D., Wang, C.-C., & Soga, K. (2025). Exploring Distributed Acoustic Sensing for Pedestrian Monitoring: Signal Characteristics and Identification. Transportation Research Record: Journal of the Transportation Research Board, 0(0).https://doi.org/10.1177/03611981251362790