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2026-05-13T16:34:30Z

CynthiaBluteau:

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2026-05-13T16:34:06Z

CynthiaBluteau: /* References */

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2026-05-13T16:33:51Z

CynthiaBluteau:

CynthiaBluteau:

Talk:Tentative benchmarks for shear probes

2022-10-17T19:10:54Z

CynthiaBluteau:

Segmenting datasets

2022-07-14T00:03:22Z

CynthiaBluteau: /* Minimum fft-length */

{{ADV processing
|instrument_type=ADV
|level=level 1 raw, level 2 segmented and quality controlled
}}
Once the raw observations have been [[Data processing of raw measurements|quality-controlled]], then you must split the time series into shorter segments by considering:
* [[Time and length scales of turbulence]]
* [[Stationarity]] of the segment and [[Taylor's Frozen Turbulence| Taylor's frozen turbulence hypothesis]]
* Required statistical significance of the resulting spectra, important mainly if you use [[Velocity decontamination by cospectral methods| cospectral or coherence-based]] methods to remove motion-induced contamination from the spectra

A good way to select the segment length is by inspecting the [[compute the spectra|computed spectra]] estimated from a 512-s long segment and an [[#fftlength|fft-length]] that is one-quarter of the segment length (128 s). Plotting these spectra against the theoretical spectral lines (see [[#specavg|Fig 2 and 3]]), enables identifying whether 1 decade of an inertial subrange is resolved with at least 8 spectral samples in this subrange.

== Considerations ==
Measurements are typically collected in the following two ways:
* continuously, or in such long [[Burst sampling|bursts]] that they can be considered continuous
* short [[Burst sampling|bursts]] that are typically at most 2-3x the expected largest [[Time and length scales of turbulence|turbulence time scales]] (e.g., 10 min in ocean environments)
This segmenting step dictates the minimum [[Burst sampling|burst]] duration when setting up your equipment. The act of chopping a time series into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. The length of the [[Segmenting datasets|segment]] in time is usually a more important consideration than [[Detrending time series#detrend_ex|detrending the time series]] when estimating <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] of the final spectra.

The shorter the segment, the higher the temporal resolution of the final <math>\varepsilon</math> time series, and the more likely the segment will be [[Stationarity|stationary]]. The segment must remain sufficiently long such that the lowest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]] are retained by the [[Compute the spectra|computed spectra]]. This is particularly important when measurement noise drowns the highest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]]. Thus, using too short segments may inadvertently render the spectra unusable for deriving <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] by virtue of no longer resolving this subrange as shown in ([[#fftlength|Fig. 1]]).

[[File:ADV_fft_length.png|none|thumbnail|500px|Fig.1 Contours represent the log of the fft-length required to resolve the non-dimensional wavenumber [rad/m] indicated in each panel's title. The inertial subrange ends at approximately <math>\hat{k}L_k\approx0.1</math> (or <math>kL_k\approx0.015</math> in cpm), and so panel (c) denotes the fft-length that resolves the end of the inertial subrange i.e., the beginning of the viscous subrange. The fft-length must be at least 10x longer (see b), preferably 50x (panel c) given the low number of spectral observations at the lowest frequencies (wavenumbers)]]

== Recommendations==
A good rule of thumb for tidally-influenced environments is 5 to 15 min segments, but this may be shorter in certain energetic and fast-moving flows ([[#fastepsi|Fig. 2]]) and longer in less energetic environments ([[#lowepsi|Fig.3]]). The final segment length is partly a function of the fft-length and the desired statistical significance (degrees of freedom) of the final [[Compute the spectra| computed spectra]]. If [[Velocity decontamination by cospectral methods| cospectral methods]] will be employed to decontaminate the velocities, then the segment length should be 4-5x larger than the [[#fftlength|fft-length]] unless band-averaging is used to [[Compute the speectra#specavg| average the (co-)spectra]].

===Minimum fft-length===
[[#fftlength|Fig. 1]] provides a guide to the fft-length required for resolving different subrange as a function of the speed past the sensor, and <math>\varepsilon</math>. For instance, an fft-length of 4 s would resolve one decade of the inertial subrange at speeds past the sensor of 0.5 m/s and <math>\varepsilon\sim10^{-7}</math> W/kg. Longer segments would be required for slower flows or lower <math>\varepsilon</math>. At <math>\varepsilon\approx10^{-9}</math> W/kg, one decade of the inertial subrange would be resolved with an fft-length longer than 10s provided the speed was faster than 0.5 m/s.

Because the inertial subrange may be contaminated at the highest wavenumbers by instrument noise, we suggest using longer segments than the minimum shown in [[#fftlength|Fig. 1b]]. This strategy also enables having a larger number of spectral observations to [[Spectral fitting|fit]] over the inertial subrange given the spectral resolution is equal to the inverse of the fft-length.

===Choosing segment-length===
The final segment length may be larger than the fft-length depending if you use block-averaging for [[Compute the spectra#specavg|computing the spectra]]. The maximum segment length should be shorter than the largest [[Time and length scales of turbulence|turbulent time scales]]. To increase the statistical reliability of the spectral observations, which is absolutely necessary when applying any [[Velocity decontamination by cospectral methods|co-spectral techniques]] for motion decontamination of spectra, we recommend segment length that is 5x the [[#fftlength|fft-length]] unless band-averaging is employed during the [[Compute the spectra#specavg| spectral averaging]]. More details about the minimum degrees of freedom are given in the [[velocity decontamination by cospectral methods]] wikipage.

{{FontColor|fg=white|bg=red|text= Are the peaks in the MAVS data vortex shedding from the rings. Check the motion sensors onboard?}}

[[File:Segment_anisotropy.png|left|thumbnail|350px|Fig. 2: Example theoretical velocity spectra for different <math>\varepsilon</math> with the empirical limit <math>\hat{k}L_k\sim0.1</math> denoted by the diamonds (<math>\hat{k}</math> is in rad/m). The inertial subrange extends to smaller wavenumber <math>k</math> [cpm] as <math>\varepsilon</math> increases. The lowest frequency resolved by a spectra is the inverse of the fft-length used when computing the spectra. The colored lines are spectral observations from a dataset with fast speeds and large <math>\varepsilon</math>. In this example, we used relatively short segments (128s) to estimate the spectra from fft-length of 32 s (2048 samples @ 64 Hz). The impact of [[Velocity inertial subrange model#anisotropy|turbulence anisotropy]] is also visible through the flattening of the spectra around 1 cpm. The secondary x-axis show the corresponding frequencies for a range of mean speeds past the sensors]]

[[File:SegmentAnisotropyLowE.png|center|thumbnail|350px|Fig. 3: Same as Fig 1 but for a different dataset with low speeds and low <math>\varepsilon</math>, requiring the use of relatively long segments (1024s) to estimate the spectra from fft-length of 512 s (4096 samples @ 8 Hz).]]

===Overlapping segments===
Using overlapping segments, i.e., obtaining your first <math>\varepsilon</math> estimate from time 0 to 5 min, and the second estimate from 2.5 to 5 min (50% overlap) essentially smoothes the final timeseries <math>\varepsilon</math>. One advantage of using overlapping segments is that you can recover estimates before and after sudden changes in flow conditions that render one segment unusable for getting <math>\varepsilon</math>. The use of overlapping segments is purely a matter of preference, and does not impact the quality of the final timeseries of epsilon.

----
Return to [[Preparing_quality-controlled_velocities|Preparing quality-controlled velocities]]

Segmenting datasets

2022-07-14T00:01:32Z

CynthiaBluteau: /* Choosing segment-length */

{{ADV processing
|instrument_type=ADV
|level=level 1 raw, level 2 segmented and quality controlled
}}
Once the raw observations have been [[Data processing of raw measurements|quality-controlled]], then you must split the time series into shorter segments by considering:
* [[Time and length scales of turbulence]]
* [[Stationarity]] of the segment and [[Taylor's Frozen Turbulence| Taylor's frozen turbulence hypothesis]]
* Required statistical significance of the resulting spectra, important mainly if you use [[Velocity decontamination by cospectral methods| cospectral or coherence-based]] methods to remove motion-induced contamination from the spectra

A good way to select the segment length is by inspecting the [[compute the spectra|computed spectra]] estimated from a 512-s long segment and an [[#fftlength|fft-length]] that is one-quarter of the segment length (128 s). Plotting these spectra against the theoretical spectral lines (see [[#specavg|Fig 2 and 3]]), enables identifying whether 1 decade of an inertial subrange is resolved with at least 8 spectral samples in this subrange.

== Considerations ==
Measurements are typically collected in the following two ways:
* continuously, or in such long [[Burst sampling|bursts]] that they can be considered continuous
* short [[Burst sampling|bursts]] that are typically at most 2-3x the expected largest [[Time and length scales of turbulence|turbulence time scales]] (e.g., 10 min in ocean environments)
This segmenting step dictates the minimum [[Burst sampling|burst]] duration when setting up your equipment. The act of chopping a time series into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. The length of the [[Segmenting datasets|segment]] in time is usually a more important consideration than [[Detrending time series#detrend_ex|detrending the time series]] when estimating <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] of the final spectra.

The shorter the segment, the higher the temporal resolution of the final <math>\varepsilon</math> time series, and the more likely the segment will be [[Stationarity|stationary]]. The segment must remain sufficiently long such that the lowest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]] are retained by the [[Compute the spectra|computed spectra]]. This is particularly important when measurement noise drowns the highest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]]. Thus, using too short segments may inadvertently render the spectra unusable for deriving <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] by virtue of no longer resolving this subrange as shown in ([[#fftlength|Fig. 1]]).

[[File:ADV_fft_length.png|none|thumbnail|500px|Fig.1 Contours represent the log of the fft-length required to resolve the non-dimensional wavenumber [rad/m] indicated in each panel's title. The inertial subrange ends at approximately <math>\hat{k}L_k\approx0.1</math> (or <math>kL_k\approx0.015</math> in cpm), and so panel (c) denotes the fft-length that resolves the end of the inertial subrange i.e., the beginning of the viscous subrange. The fft-length must be at least 10x longer (see b), preferably 50x (panel c) given the low number of spectral observations at the lowest frequencies (wavenumbers)]]

== Recommendations==
A good rule of thumb for tidally-influenced environments is 5 to 15 min segments, but this may be shorter in certain energetic and fast-moving flows ([[#fastepsi|Fig. 2]]) and longer in less energetic environments ([[#lowepsi|Fig.3]]). The final segment length is partly a function of the fft-length and the desired statistical significance (degrees of freedom) of the final [[Compute the spectra| computed spectra]]. If [[Velocity decontamination by cospectral methods| cospectral methods]] will be employed to decontaminate the velocities, then the segment length should be 4-5x larger than the [[#fftlength|fft-length]] unless band-averaging is used to [[Compute the speectra#specavg| average the (co-)spectra]].

===Minimum fft-length===
[[#fftlength|Fig. 1]] provides a guide to the fft-length required for resolving different subrange as a function of the speed past the sensor, and <math>\varepsilon</math>. For instance, an fft-length of 4 s would resolve one decade of the inertial subrange at speeds past the sensor of 0.5 m/s and <math>\varepsilon\sim10^{-7}</math> W/kg. Longer segments would be required for slower flows or lower <math>\varepsilon</math>. At <math>\varepsilon\approx10^{-9}</math> W/kg, one decade of the inertial subrange would be resolved with an fft-length longer than 10s provided the speed was faster than 0.5 m/s.

Because the inertial subrange may be contaminated at the highest wavenumbers by instrument noise, we suggest using longer segments than the minimum shown in [[#fftlength|Fig. 1b]]. This strategy also enables having a larger number of spectral observations to fit over the inertial subrange given the spectral resolution also depends on the fft-length.

===Choosing segment-length===
The final segment length may be larger than the fft-length depending if you use block-averaging for [[Compute the spectra#specavg|computing the spectra]]. The maximum segment length should be shorter than the largest [[Time and length scales of turbulence|turbulent time scales]]. To increase the statistical reliability of the spectral observations, which is absolutely necessary when applying any [[Velocity decontamination by cospectral methods|co-spectral techniques]] for motion decontamination of spectra, we recommend segment length that is 5x the [[#fftlength|fft-length]] unless band-averaging is employed during the [[Compute the spectra#specavg| spectral averaging]]. More details about the minimum degrees of freedom are given in the [[velocity decontamination by cospectral methods]] wikipage.

{{FontColor|fg=white|bg=red|text= Are the peaks in the MAVS data vortex shedding from the rings. Check the motion sensors onboard?}}

[[File:Segment_anisotropy.png|left|thumbnail|350px|Fig. 2: Example theoretical velocity spectra for different <math>\varepsilon</math> with the empirical limit <math>\hat{k}L_k\sim0.1</math> denoted by the diamonds (<math>\hat{k}</math> is in rad/m). The inertial subrange extends to smaller wavenumber <math>k</math> [cpm] as <math>\varepsilon</math> increases. The lowest frequency resolved by a spectra is the inverse of the fft-length used when computing the spectra. The colored lines are spectral observations from a dataset with fast speeds and large <math>\varepsilon</math>. In this example, we used relatively short segments (128s) to estimate the spectra from fft-length of 32 s (2048 samples @ 64 Hz). The impact of [[Velocity inertial subrange model#anisotropy|turbulence anisotropy]] is also visible through the flattening of the spectra around 1 cpm. The secondary x-axis show the corresponding frequencies for a range of mean speeds past the sensors]]

[[File:SegmentAnisotropyLowE.png|center|thumbnail|350px|Fig. 3: Same as Fig 1 but for a different dataset with low speeds and low <math>\varepsilon</math>, requiring the use of relatively long segments (1024s) to estimate the spectra from fft-length of 512 s (4096 samples @ 8 Hz).]]

===Overlapping segments===
Using overlapping segments, i.e., obtaining your first <math>\varepsilon</math> estimate from time 0 to 5 min, and the second estimate from 2.5 to 5 min (50% overlap) essentially smoothes the final timeseries <math>\varepsilon</math>. One advantage of using overlapping segments is that you can recover estimates before and after sudden changes in flow conditions that render one segment unusable for getting <math>\varepsilon</math>. The use of overlapping segments is purely a matter of preference, and does not impact the quality of the final timeseries of epsilon.

----
Return to [[Preparing_quality-controlled_velocities|Preparing quality-controlled velocities]]

Segmenting datasets

2022-07-13T23:53:06Z

CynthiaBluteau: /* Overlapping segments */

{{ADV processing
|instrument_type=ADV
|level=level 1 raw, level 2 segmented and quality controlled
}}
Once the raw observations have been [[Data processing of raw measurements|quality-controlled]], then you must split the time series into shorter segments by considering:
* [[Time and length scales of turbulence]]
* [[Stationarity]] of the segment and [[Taylor's Frozen Turbulence| Taylor's frozen turbulence hypothesis]]
* Required statistical significance of the resulting spectra, important mainly if you use [[Velocity decontamination by cospectral methods| cospectral or coherence-based]] methods to remove motion-induced contamination from the spectra

A good way to select the segment length is by inspecting the [[compute the spectra|computed spectra]] estimated from a 512-s long segment and an [[#fftlength|fft-length]] that is one-quarter of the segment length (128 s). Plotting these spectra against the theoretical spectral lines (see [[#specavg|Fig 2 and 3]]), enables identifying whether 1 decade of an inertial subrange is resolved with at least 8 spectral samples in this subrange.

== Considerations ==
Measurements are typically collected in the following two ways:
* continuously, or in such long [[Burst sampling|bursts]] that they can be considered continuous
* short [[Burst sampling|bursts]] that are typically at most 2-3x the expected largest [[Time and length scales of turbulence|turbulence time scales]] (e.g., 10 min in ocean environments)
This segmenting step dictates the minimum [[Burst sampling|burst]] duration when setting up your equipment. The act of chopping a time series into smaller subsets, i.e., segments, is effectively a form of low-pass (box-car) filtering. The length of the [[Segmenting datasets|segment]] in time is usually a more important consideration than [[Detrending time series#detrend_ex|detrending the time series]] when estimating <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] of the final spectra.

The shorter the segment, the higher the temporal resolution of the final <math>\varepsilon</math> time series, and the more likely the segment will be [[Stationarity|stationary]]. The segment must remain sufficiently long such that the lowest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]] are retained by the [[Compute the spectra|computed spectra]]. This is particularly important when measurement noise drowns the highest wavenumber (frequencies) of the [[Velocity inertial subrange model|inertial subrange]]. Thus, using too short segments may inadvertently render the spectra unusable for deriving <math>\varepsilon</math> from the [[Velocity inertial subrange model|inertial subrange]] by virtue of no longer resolving this subrange as shown in ([[#fftlength|Fig. 1]]).

[[File:ADV_fft_length.png|none|thumbnail|500px|Fig.1 Contours represent the log of the fft-length required to resolve the non-dimensional wavenumber [rad/m] indicated in each panel's title. The inertial subrange ends at approximately <math>\hat{k}L_k\approx0.1</math> (or <math>kL_k\approx0.015</math> in cpm), and so panel (c) denotes the fft-length that resolves the end of the inertial subrange i.e., the beginning of the viscous subrange. The fft-length must be at least 10x longer (see b), preferably 50x (panel c) given the low number of spectral observations at the lowest frequencies (wavenumbers)]]

== Recommendations==
A good rule of thumb for tidally-influenced environments is 5 to 15 min segments, but this may be shorter in certain energetic and fast-moving flows ([[#fastepsi|Fig. 2]]) and longer in less energetic environments ([[#lowepsi|Fig.3]]). The final segment length is partly a function of the fft-length and the desired statistical significance (degrees of freedom) of the final [[Compute the spectra| computed spectra]]. If [[Velocity decontamination by cospectral methods| cospectral methods]] will be employed to decontaminate the velocities, then the segment length should be 4-5x larger than the [[#fftlength|fft-length]] unless band-averaging is used to [[Compute the speectra#specavg| average the (co-)spectra]].

===Minimum fft-length===
[[#fftlength|Fig. 1]] provides a guide to the fft-length required for resolving different subrange as a function of the speed past the sensor, and <math>\varepsilon</math>. For instance, an fft-length of 4 s would resolve one decade of the inertial subrange at speeds past the sensor of 0.5 m/s and <math>\varepsilon\sim10^{-7}</math> W/kg. Longer segments would be required for slower flows or lower <math>\varepsilon</math>. At <math>\varepsilon\approx10^{-9}</math> W/kg, one decade of the inertial subrange would be resolved with an fft-length longer than 10s provided the speed was faster than 0.5 m/s.

Because the inertial subrange may be contaminated at the highest wavenumbers by instrument noise, we suggest using longer segments than the minimum shown in [[#fftlength|Fig. 1b]]. This strategy also enables having a larger number of spectral observations to fit over the inertial subrange given the spectral resolution also depends on the fft-length.

===Choosing segment-length===
The final segment length may be larger than the fft-length depending if you use block-averaging for [[Compute the spectra#specavg|computing the spectra]]. The maximum segment length should be shorter than the largest [[Time and length scales of turbulence|turbulent time scales]]. To increase the statistical reliability of the spectral observations, which is absolutely necessary when applying any [[Velocity decontamination by cospectral methods|co-spectral techniques]] for motion decontamination of spectra, we recommend segment length that is 5x the [[#fftlength|fft-length]] unless band-averaging is employed during the [[Compute the spectra#specavg| spectral averaging]]. More details about the minimum degrees of freedom are given in the [[[velocity decontamination by cospectral methods]] wikipage.

{{FontColor|fg=white|bg=red|text= Are the peaks in the MAVS data vortex shedding from the rings. Check the motion sensors onboard?}}

[[File:Segment_anisotropy.png|left|thumbnail|350px|Fig. 2: Example theoretical velocity spectra for different <math>\varepsilon</math> with the empirical limit <math>\hat{k}L_k\sim0.1</math> denoted by the diamonds (<math>\hat{k}</math> is in rad/m). The inertial subrange extends to smaller wavenumber <math>k</math> [cpm] as <math>\varepsilon</math> increases. The lowest frequency resolved by a spectra is the inverse of the fft-length used when computing the spectra. The colored lines are spectral observations from a dataset with fast speeds and large <math>\varepsilon</math>. In this example, we used relatively short segments (128s) to estimate the spectra from fft-length of 32 s (2048 samples @ 64 Hz). The impact of [[Velocity inertial subrange model#anisotropy|turbulence anisotropy]] is also visible through the flattening of the spectra around 1 cpm. The secondary x-axis show the corresponding frequencies for a range of mean speeds past the sensors]]

[[File:SegmentAnisotropyLowE.png|center|thumbnail|350px|Fig. 3: Same as Fig 1 but for a different dataset with low speeds and low <math>\varepsilon</math>, requiring the use of relatively long segments (1024s) to estimate the spectra from fft-length of 512 s (4096 samples @ 8 Hz).]]

===Overlapping segments===
Using overlapping segments, i.e., obtaining your first <math>\varepsilon</math> estimate from time 0 to 5 min, and the second estimate from 2.5 to 5 min (50% overlap) essentially smoothes the final timeseries <math>\varepsilon</math>. One advantage of using overlapping segments is that you can recover estimates before and after sudden changes in flow conditions that render one segment unusable for getting <math>\varepsilon</math>. The use of overlapping segments is purely a matter of preference, and does not impact the quality of the final timeseries of epsilon.

----
Return to [[Preparing_quality-controlled_velocities|Preparing quality-controlled velocities]]

2022-07-11T15:25:49Z

CynthiaBluteau: Added wikilcnks

To compute the spectrum of the turbulent velocity fluctuations, you need to:
# Determine appropriate [[#fftlength|fft-length]] and [[#specavg|spectral averaging]] for each data [[Segmenting datasets|segment]]
# Compute the spectrum using standard techniques <ref name="EmeryThomson2001">{{Cite journal
|authors= Emery, W. J., and R. E. Thomson
|journal_or_publisher= Elsevier
|paper_or_booktitle= Data analysis methods in physical oceanography, 2nd edition, Section 5.6.7-5.6.8
|year= 2001
|doi=(ISBN)9780080477008
}}</ref><ref name="Priestly1981">{{Cite journal
|authors= Priestly M.B.
|journal_or_publisher= Academic Press
|paper_or_booktitle= Spectral analysis and time series: Multivariate series prediction and control
|year= 1981
|doi=(ISBN)0125649010
}}</ref>
# Convert the spectrum from the time domain to the space domain using the mean speed past the sensor {{FontColor|fg=white|bg=red|text= only for steady flows, not required for surface wave analysis}}
# Compute degrees of freedom (dof) and confidence intervals of the final spectra <ref name="EmeryThomson2001"/> based on the assumption that the spectra observations are <math>\chi</math>-squared distributed i.e., the turbulent velocities are gaussian (normally distributed).

==Spectral averaging techniques==
Each segment is often subdivided into smaller [[#fftlength|fft-length]] long chunks (50% overlap), which are then windowed before estimating numerous spectra (FFT) that are block-averaged for increased statistical significance. Another averaging strategy is band-averaging spectra in the frequency domain, which allows the [[Segmenting datasets|segment length]] to be the same as the [[#fftlength|fft-length]]. A combination of both strategies is also possible. The final strategy depends on whether you need increased statistical significance for correcting motion-contaminated spectra using [[Velocity decontamination by cospectral methods|cospectral methods]], and the lowest frequencies (wavenumbers) you want to resolve.

The spectrum's lowest resolved frequency and final resolution are the inverses of the [[#fftlength| fft-length]]. The [[#fftlength|fft-length]] dictates the lowest frequencies resolved by the spectra, while the Nyquist frequency (half the sampling rate) dictates the largest frequency of the spectra. Whether these high and low frequencies are used to estimate <math>\varepsilon</math> depends on the measurement quality and whether they are located in the inertial subrange, respectively.

{{FontColor|fg=white|bg=red|text= Remove redundant info from [[Segmenting datasets]], and add references to figure summary page}}

[[File:Spectra computation.png|thumbnail|800px|Example vertical velocity spectra estimated from a 128-s long segment of observations, which highlights the spectral bandwidth and resolution using different spectral averaging strategies. Velocity spectra The original spectra (black) were estimated using 7 fft blocks, each 32 s long with a 50% overlap and a Hanning window applied on each block in the time-domain (21 degrees of freedom). The colored lines are spectra computed from the same segment but using alternate spectral averaging strategies. In red, the fft-length was halved to 16 s (43 degrees of freedom), while the third example (in purple) uses a combination of block and band averaging with the same number of blocks as the first example (black) but three adjacent frequencies were averaged together in the frequency domain increasing the degrees of freedom to 58. Note: the lowest frequencies of this spectra example are likely outside the inertial subrange as the peaks are almost statistically significant i.e., there's a deterministic signature at the lowest frequencies. Spectral-fitting algorithms can skip these frequencies, so this does not pose an issue for estimating <math>\varepsilon</math>]]

==References==

[[Category:Velocity point-measurements]]