Spectral density and average frequency

In summary, the conversation discusses solving Equation 10.25 for the mean angular frequency. The equation involves the spectral density y(x) and angular frequency x. The individual has data for y(x) and x and is attempting to use MATLAB to solve for the mean angular frequency. They have attempted to calculate the numerator and denominator using the trapz(x,y) function, but are not getting the correct answer. They are seeking help to identify their mistake.
  • #1
doop4
4
0
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!
 
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  • #2
Is this schoolwork or work-work? It needs to be posted in different places, depending.

Quiz Question -- Why?
 
  • #3
It's sort of "home work" of a grad. Any ideas on a solution?
 

1. What is spectral density?

Spectral density is a measure of the distribution of power (or energy) in a signal over a range of frequencies. It is a fundamental concept in signal processing and is often used to analyze and characterize signals in various fields such as physics, engineering, and statistics.

2. How is spectral density calculated?

The spectral density of a signal can be calculated by taking the Fourier transform of the signal, which represents the signal in the frequency domain. The squared magnitude of the Fourier transform at a particular frequency represents the power or energy at that frequency, and the spectral density is the Fourier transform multiplied by its complex conjugate.

3. What is the relationship between spectral density and average frequency?

Average frequency, also known as center frequency, is the frequency at which the spectral density is highest. In other words, it is the frequency at which the most power or energy is concentrated in the signal. The spectral density and average frequency are directly related, as the spectral density plot shows how the power or energy is distributed across different frequencies, and the average frequency indicates the frequency with the highest concentration of power.

4. How is spectral density used in practical applications?

Spectral density is a useful tool in various applications such as signal processing, communication systems, and data analysis. It can help identify patterns and characteristics in signals, filter out noise, and extract useful information from signals. Spectral density is also used in fields such as physics and engineering to study the behavior of systems and phenomena in the frequency domain.

5. Can spectral density be used for non-periodic signals?

Yes, spectral density can be used for non-periodic signals as well. In this case, the spectral density is calculated using the power spectral density (PSD) function, which is a mathematical representation of the spectral density for non-periodic signals. The PSD is calculated using the autocorrelation function of the signal, which measures the similarity between the signal and a delayed version of itself at different time intervals. Therefore, spectral density can be used for both periodic and non-periodic signals.

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