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Re: power spectrum

• To: mathgroup at smc.vnet.net
• Subject: [mg52742] Re: [mg52695] power spectrum
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Sat, 11 Dec 2004 05:22:05 -0500 (EST)
• References: <200412100123.UAA18915@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On Dec 9, 2004, at 8:23 PM, George Szpiro wrote:

> If I have a string of data - let us say a time series of 200  
> observations -
> how can I find the power spectrum? I did Fourier[list] but have no  
> idea what
> the output means.
>
> Thank you for any help (please to my email address:
> george at netvision.net.il)
>

If your data is real valued

ListPlot[Abs[Fourier[list]][[Range[Quotient[Length[list],2]+1]]],PlotJoi 
ned->True]

will give you the power spectrum from frequencies 0 to half your sample  
rate.

For complex valued observations

ListPlot[Abs[RotateRight[Fourier[list],Quotient[Length[list],2]]],PlotJo 
ined->True]

will give you the power spectrum from -1/2*sample rate to 1/2*sample  
rate - 1/(Length[list] * sample rate).

As for what it all means, section 13.4 of Numerical Recipes  
(http://lib-www.lanl.gov/numerical/index.html) explains power spectra.

Regards,

Ssezi

• References:
  • power spectrum
    • From: George Szpiro <george@netvision.net.il>