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August 31, 2010, 19:39 
power spectral density

#1 
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Naveen
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Hello,
I am carrying out a two dimensional simulation in a geometry with Nx X Ny number of grid points in stream wise and cross stream directions. At every time step I write the value of stream wise velocity component at a particular grid point into a datafile, I run for about 2 million time steps with a step size of 5e04. At the end of the run, I have a time signal of this stream wise velocity component at that particular grid point. The figure in the attached file shows the variation of u component with time at that particular location, now I want to see this signal on power  frequency plane, after lot of googling I found that if the signal is periodic one should go for power spectrum whereas if the signal is aperiodic one should go for power spectral density (is it true?). So I used the function pwelch in MATLAB to get the PSD which is also shown in attached file, but as per the definition PSD just gives the power between two frequencies but what I want to see is peaks at dominating frequencies and very small values at others, can someone please tell me how can I get it. Thank you Vetnav 

September 1, 2010, 20:29 

#2 
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Naveen
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Hello
Is there any one who can help me with this? thanks 

September 2, 2010, 11:22 
Try...

#3 
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Tomer
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Try Indirectly to FFT the signal and than extract PSD. Matlab usualy has a straiforward Help Guide but still one should be sure of the math behind the operator used.


September 2, 2010, 11:30 
Thanks

#4 
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Naveen
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Thank u Tomer for the reply, but I am not looking for the PSD, I want to see peaks at some particular frequencies (like a peak at 10Hz on power vs. frequency plot for a 10 Hz sine wave), PSD does not give this, it just gives total amount of power contained between two different frequencies.
Thanks 

September 2, 2010, 12:02 

#5 
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Tomer
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I dont realy understand... If lets say you signal is composed only from a superposition of sine waves you would idealy get a sharp discrete frequency peaks via PSD in the proper fr., on the other hand white noise would give you a band with average frequency content.
now you should ask if the data you aquired is ergodicm otherwise frequancy analysis is somewhat meaningless 

September 2, 2010, 12:44 

#6 
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Naveen
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Thanks for the reply, You seem to be expert in this kind of stuff, but as per me I am doing this for the first time that is why I am using MATLAB. But reading your suggestions I am really lost now .
Let me think more and ask. Thanks Naveen 

September 3, 2010, 01:47 

#7 
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Tomer
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Another suggestion which might achieve the goal of watching the frequency "at a particular time" is using wavelet transform methods.
Under some restrictions (ergodicity, sampling rate, etc...) by tuning its parameters it will allow you to get somewhat of "time  frequency" contour map which will enable you to view to some extent the energy content of a specific frequency and time (you might look at it as E=E(f,t)) . Of course the Idea of E=E(f,t) is somewhat an otopic idea for when applying the transform (which might be considered as somewhat of a moving gaussian windowing) tou get both frequency content and time content of the energy "smudged". 

September 3, 2010, 08:08 
Time Serie Analysis

#8 
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Nicholas F Camus
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Dear Vetnav,
Tomer has it right. There is a wealth of analysis you can do with such a timeseries. The first thing you should try (Tomer has suggested this), is to take the Fourier Transform of your time series; this will provide you with real and imaginary parts in frequencyperiod space. Take the sum of these parts squared and you have the power spectrum, this will tell you the quasiperiods present in your timeseries (the real part should do this alone). To analyse if there are any dominant noise processes at work you could use a structure function. Structure function analysis provides a method of quantifying time variability without the problem of aliasing, or windowing, that are encountered using the traditional FFT technique. Potentially it is able to provide information on the nature of the process that causes variability. The method is mainly concerned with the categorization of underlying noise processes and the identification of correlation timescales. Finally the mother of all analysis tools. Wavelets. Check out Torrence and Compo's website for all the information you need on these. Wavelets essentailly not only tell you if periodicity exists in your timeseries but when it exists (temporal nature of the fluctuations). Please contact me if you require further information and I will send you a PDF of a papar of mine... Cheers, Cam 

September 3, 2010, 14:28 

#9 
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Naveen
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Dear Tomer and Killercam
Thank you very much for the help, I calculated it again and I have more questions now looking at the result, I will go through the website that killercam suggested, but I want to ask you guys some more questions I prepared a document which contains different figures and its size is bigger than the upload limit here so can you please provide me your email ids? If you don't want to write your email ids here, u can email me at vnaveen at ucla dot edu Thank you Naveen 

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