Calculate auto spectral density and cross spectral density of a time series data in excel

I'm a beginner to spectral analysis and MATLAB. I'm asked to calculate auto spectral density and cross spectral density of a time series values saved in excel.

I'll explain the data that I have in excel. First column corresponds to time steps, second column is water elevation (for which auto spectral density (Sxx)) and third column is responses (for which cross spectral density(Sxy) with water elevation). The time step is 0.0125.

Data starts from 0 s to 3600 s.

I tried using periodogram, however i'm confused with the understanding of it.

Could someone help me and explain me, how to get Sxx and Sxy, with MATLAB inbuilt functions and without inbuilt functions?

Please give reference equations that is used.

Any help is highly appreciated.

Answer 1

[Balasundaram Mohan]

Hi, It is mean square of individual spectrum you have obtained. Like you have FFT for a time series and take complex conjugate and multiply both and then take mean of it. you will get auto spectral density. The same with two different time series will give you cross spectral density. Effectively it is a mean-square value over a band width of your interest. But still I urge you to take a look at in any of standard text book in time series analysis or signal processing.

Best Balasundaram Mohan

Answer 2

[Dawn Ward]

Hi Vijay kg, I am trying to do exactly the same, for a floating wind turbine. Did you find out how to get the Sxx and Sxy from the excel data? Thanks, Dawn

Answer 3

[vijay kg]

Hi Dawn Ward,

I still didn't find the answer for it. Please let me know if you happen to get it in near future. My email is [e-mail]. Get in touch to discuss more.