Fft-length: Difference between revisions
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fft-length | {{DefineConcept | ||
|description=fast Fourier transform length | |||
|article_type=Concepts | |||
}} | |||
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>\varepsilon</math> values (<math>\sim 10^{-10}</math> W/kg) require spectra down to 0.5 to 1 cpm. Moderate rates (<math>10^{-8}</math> to <math>10^{-7}</math> W/kg) require resolutions of <math>\sim</math>1 cpm, while higher rates require <math>\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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return to [[Flow chart for shear probes]] | |||
[[Category:Shear probes]] | |||
Latest revision as of 20:11, 6 June 2024
| 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.
{{#default_form:DefineConcept}} {{#arraymap:|,|x||}}
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>\varepsilon</math> values (<math>\sim 10^{-10}</math> W/kg) require spectra down to 0.5 to 1 cpm. Moderate rates (<math>10^{-8}</math> to <math>10^{-7}</math> W/kg) require resolutions of <math>\sim</math>1 cpm, while higher rates require <math>\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.
return to Flow chart for shear probes
