Fft-length
| Short definition of Fft-length |
|---|
| fast Fourier transform length |
This is the common definition for Fft-length, but other definitions maybe discussed within the wiki.
The lowest wavenumber that one wishes to resolve in a spectrum is determined by the length (in units of meters) of the segments of data that are processed by a fast Fourier transform.
The lowest wavenumber resolved by a spectrum is the inverse of the length of the fft-segments.
This choice is influenced by the (so far mostly unknown) rate of dissipation, statistical reliability, and the length of the vehicle that carries the shear probe.
Very low [math]\displaystyle{ \varepsilon }[/math] values ([math]\displaystyle{ \sim 10^{-10} }[/math] W/kg) require spectra down to 0.5 to 1 cpm. Moderate rates ([math]\displaystyle{ 10^{-8} }[/math] to [math]\displaystyle{ 10^{-7} }[/math] W/kg) require resolutions of [math]\displaystyle{ \sim }[/math]1 cpm, while higher rates require [math]\displaystyle{ \sim }[/math]2 cpm.
A fairly common processing technique is to window each fft segment with a cosine bell and to overlap the segments by 50%. The degrees of freedom (dof) produced by this method is 1.9 times the number of fft segments used to estimate the spectrum. The statistical reliability of a spectrum increases with the number of dof. Thus, the ratio of dissipation length to fft length is also driven by the statistical reliability that you wish to achieve. As a general rule, this ratio should never be less than 2, and a ratio of 5 or larger is highly desirable. Finally, the length of the vehicle that carries the shear probe also sets a lower limit to the wavenumber of shear that can be resolved. The fft-length should never exceed the length of the profiler, unless the profiler is a rigidly fixed platform that is not swayed by the eddies in the flow.
return to Flow chart for shear probes
