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January 14, 2004, 04:54 
fft of unsteady solution

#1 
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I have questions to you about FFT of unsteady solution.
I had acquired unsteady solution from 3D DES simulation. I want to search the Stouhal number at one point from FFT. So I obtained the velocity history about 5000 time step(approximately 200 period). However the frequency is not unique and have so many peaks and the peak frequencies are different according to the range selected. Q1) In general, how many periods are needed for FFT ? Q2) If I have 4096(2^12) data, these 4096 data is totally done from a FFT ? Or 4 data set of 1024 data are done from FFT and averaged ? Q3) If the peak frquency is different according to the range(approximately 50 periods) selected, the solution is not converged ?? Thank you in advance. 

January 14, 2004, 05:38 
Re: fft of unsteady solution

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I would suggest doing something more rigorous like:
1) Work out your minimum required frequency. Use it to choose the sample length. From experience, make your sample long enough to contain at least two cycles of the minimum frequency required. Assuming that 1024 points is long enough... 2) Divide your time history into 8 sets of 1024 points so that there is 50% overlap between sets. 3) Multiply each set by a Hanning window (it's unlikely that your data is cyclic within the window). 4) Take the mean of the autopowers of the time histories (autopower = Fx . conj(Fx) where Fx is the complex spectrum). Square root it to get your spectrum. 5) Scale your data to account for the window: multply the spectrum by 2 to get the amplitudes right or by sqrt(8/3) to get the energy right (if you are summing across bands). HTH  Steve 

January 14, 2004, 08:55 
Re: fft of unsteady solution

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Try also:
http://www.dspguide.com/specanal.htm This is a section from a well and clearly written online DSP book.  Steve 

January 14, 2004, 20:48 
Re: fft of unsteady solution

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Thank you for your explanation.
I have one more question. In DNS or LES simulation, above methods are adopted?? I can't search the general methods about fft of unsteady solution in CFD. Any good reference ?? Thank you. 

January 15, 2004, 05:22 
Re: fft of unsteady solution

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Sorry, can't really help any more. My knowledge of signal processing isn't really in the CFD field, although I'm sure the same basic principles apply to postprocessing simulated data as do to postprocessing measured data.


January 15, 2004, 05:43 
Re: fft of unsteady solution

#6 
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Thank you very much.
Your site is very helpful to me. Thanks again. ^^ 

January 15, 2004, 07:42 
Re: fft of unsteady solution

#7 
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It's not my site. I just share a Christian name with the author!


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