POWER SPECTRUM 2D FIELD

Is there someone who can help me to calculate and plot the power spectrum of a 2D field? I have already calculated the power spectral density (it's a 3D function) of the matrix through the FFt of the same matrix, you can use various techniques, for example using the periodogram, but now i need the power spectrum of the field so...? How can i do?

(PS: for example in turbulence you give a 3D field and you can compute the power spectra, how? Therefore I am in the 2D input case)

Is there someone who have already done any Matlab or Mathematica routine?

Thank you very much,

Matteo.

_______________________________________________________ Matteo Convertino

PhD student, advisors: Prof. Andrea Rinaldo and Prof. Amos Maritan IMAGE Dept. and International Center for Hydrology "Dino Tonini" Via Loredan 20, I-35131 Padova Graduate School in Civil and Environmental Engineering Sciences University of Padova, Italy

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I am not at all sure that I can offer anything of help on this topic.

Still, it is depressing when a well-intended query simply 'hangs in the air' with no response at all. Perhaps I can encourage some more helpful input.

Starting with a one dimensional system. Suppose I apply a microphone to an oscilloscope. Then I can see a waveform that varies in amplitude with time. I can describe this as a 2-D graph of amplitude versus time.

If I square the amplitude values, the resulting graph depicts intensity or power versus time in 2D.

If I analyze the waveform into its constituent frequencies, I obtain a graph of amplitude or intensity versus frequency.

If I wish to see how this spectrum varies as time passes I need to depict a third dimension, either with a false depth on a flat page, or as is customary in the audio sonogram, by depicting greater intensity with heavier tones on the graph.

This is how language and bird song tends to be presented.

In your case, you may have a cross-section of turbulent flow in a water stream, or possibly a control volume of turbulent water, about which you would like to know how energy varies with frequency, how energy varies with X,Y position in a cross-section, or even energy in particles given by X, Y, Z space coordinates in a given volume. Then because turbulent motion is time varying - you may actually want to define parameters with position, frequncy and time. Hmmm I've mentioned X, Y, Z, Time, Frequency, amplitude, intensity, power, energy......

It is not quite clear to me exactly which of these possibilities you have in mind. So probably the most useful thing I can offer is to suggest you carefully think about exactly what you want to depict.

To say 2D or 3D is insufficient: I have already mentioned eight or nine dimensions along which you might want to compute data.....

Good luck

Brian Whatcott Altus OK