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.
FFT length is the number of samples used to compute the fast Fourier Transform. It is recommended that the displacement of the vehicle during fft-length (converted in second) should not exceed the length of the profiler, unless the profiler is a rigidly fixed platform that is not swayed by the eddies in the flow. FFT length should be [math]2^N[/math] where N is the power of 2 the closest to time required for the vehicle to travel over a full body length. Consequently, the FFT-length and length of the vehicle sets a lower limit to the wavenumber of shear that can be resolved.
Additional considerations
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.
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