Essentailly what I am interested is to solve Equation 10.25 in the following link(adsbygoogle = window.adsbygoogle || []).push({});

<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!

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# Spectral density and average frequency

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