Compute the spectra

To compute the spectrum of the turbulent velocity fluctuations, you need to:

• Determine appropriate fft-length and their overlap when averaging spectra within each data segment
• Compute the spectrum
• Convert the spectrum from the time domain to the space domain using the mean speed past the sensor only for steady flows, not required for surface wave analysis
• Compute degrees of freedom (dof) and confidence/significance levels of the final spectra.

Placeholder Example spectra

The spectrum's lowest resolved frequency and final resolution are the inverse of the fft-length, i.e., the duration of the signal used to construct the spectrum. The spectra are often estimated by block averaging numerous spectra (FFT) estimated from smaller chunks of data within each segment. Another strategy is band-averaging spectra in the frequency domain. The fft-length i.e., the duration of data used to estimate each spectrum, is thus an important quantity that dictates the final range of frequencies resolved by the spectra.

• Add significance levels on spectra
• Coherence stuff for motion contamination (must be own page)

Add an example spectra with fft shown, 2nd axis for frequencies. Another band-averaged spectra?. Remove redundant info from Segmenting datasets

Example vertical velocity spectra highlighting the spectral bandwidth and resolution using different spectral averaging strategy.

References

• Section 5.6.7 in Emery & Thomson has reference for band vs block averaging (2nd ed, p450).
• Confidence levels on p. 453 5.6.8
• Summary of spectral estimates on p.461