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Spectral density and average frequency

  1. Oct 8, 2009 #1
    Essentailly what I am interested is to solve Equation 10.25 in the following link

    <http://books.google.co.uk/books?id=Hwb5D60vb5IC&pg=PA701&lpg=PA701&dq=%22mean+angular+frequency%22&source=bl&ots=dSH6fzeZNC&sig=GB5J8nwpLCIULGhAHZLAm0RxgLM&hl=en&ei=NubNSpKqO92NjAeqwKmHBA&sa=X&oi=book_result&ct=result&resnum=9#v=onepage&q=%22mean%20angular%20frequency%22&f=false>

    ie. solve for the mean angular frequency. Let's call it x' where

    x'=integral(x*y(x).dx)/integral(y(x).dx) % Equation 10.25 where y(x) is the spectral density and x is the angular frequency.

    I have data for the spectral density values for a given angular frequency


    y=[6.2770
    10.5137
    14.8385
    19.2196
    21.5972
    19.6632
    15.2690
    10.9238
    6.5569]

    x=[ 2.6097
    2.6158
    2.6259
    2.6314
    2.6501
    2.6615
    2.6633
    2.6654
    2.6659]

    How can I solve for x' using the above data in Matlab?

    My understanding is that the numerator is essentially:

    sum[x*y(x)] for the given values of x and y (ie a weighted form ). therefore I have

    numerator=x.*y;

    the bottom is the integral so i tried using the matlab function trapz(x,y) to calculate that as well.

    denominator =trapz(x,y);

    therefore x'=numerator/denominator

    But the answer I get is incorrect. I am not sure where my mistake is. Any help will be much appreciated!
     
  2. jcsd
  3. Oct 9, 2009 #2

    berkeman

    User Avatar

    Staff: Mentor

    Is this schoolwork or work-work? It needs to be posted in different places, depending.

    Quiz Question -- Why?
     
  4. Oct 9, 2009 #3
    It's sort of "home work" of a grad. Any ideas on a solution?
     
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