Detrending time series: Difference between revisions
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In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal. | In the context of analysing turbulence observations, the resulting detrended signal should be [[Stationarity|stationary]] and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal. | ||
[[File:Long timeseries.png|thumb | [[File:Long timeseries.png|400px|thumb|Measured velocities at 4 Hz from an [[Acoustic-Doppler Velocimeters]] have been detrended using three different techniques. Empirical modal decomposition (EMD) <ref name="Wuetal_PNAS">{{Cite journal | ||
|authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng | |authors=Zhaohua Wu, Norden E. Huang, Steven R. Long, and Chung-Kang Peng | ||
|journal_or_publisher=PNAS | |journal_or_publisher=PNAS | ||
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}}</ref>, linear trend, and a 2nd order low-pass Butterworth filter. A cut-off period of 10 min was targeted by both the filter and EMD]] | }}</ref>, linear trend, and a 2nd order low-pass Butterworth filter. A cut-off period of 10 min was targeted by both the filter and EMD]] | ||
There is no exact definition for what consists of a "trend", nor any set algorithm for identifying the trend. The following techniques can be used for detrending <ref name=Wuetal_PNAS/>: | |||
# Linear trend removal | |||
# Low-pass linear filters | |||
# Empirical modal decomposition | |||
The first two methods presume the original time series is [[Stationarity|stationary]] and linear, while the third is adaptive and applicable to nonlinear and non-stationary time series. Note that chopping a time series into smaller subsets, i.e., segments, is essentially a form of low-pass (box-car) filtering. | |||
==Notes== | ==Notes== | ||
Revision as of 14:11, 30 November 2021
| Short definition of Detrending time series |
|---|
| Detrending typically refers to removing the low-frequency content of the time series |
This is the common definition for Detrending time series, but other definitions maybe discussed within the wiki.
In the context of analysing turbulence observations, the resulting detrended signal should be stationary and contain mostly contributions from turbulence and surface waves (if present). However, frame interference (wakes), vibrations and measurement noise may also contaminate the detrended signal.
There is no exact definition for what consists of a "trend", nor any set algorithm for identifying the trend. The following techniques can be used for detrending [1]:
- Linear trend removal
- Low-pass linear filters
- Empirical modal decomposition
The first two methods presume the original time series is stationary and linear, while the third is adaptive and applicable to nonlinear and non-stationary time series. Note that chopping a time series into smaller subsets, i.e., segments, is essentially a form of low-pass (box-car) filtering.
Notes
- ↑ 1.0 1.1 Zhaohua Wu, Norden E. Huang, Steven R. Long and and Chung-Kang Peng. 2007. On the trend, detrending, and variability of nonlinear and nonstationary time series. PNAS. doi:10.1073/pnas.0701020104
