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From: "Dave Robinson" <dave.robinson@somewhere.biz>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT - Output to RMS Equivalents
Date: Fri, 2 May 2008 14:27:03 +0000 (UTC)
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"John Costello" <JohnCostello@ChampAero.com> wrote in 
message <fvf4jm$4df$1@fred.mathworks.com>...
> I need some help converting the Matlab FFT output into 
> equivalent RMS levels for signal analysis.
> 
> I have numerical data from an oscilloscope that has three 
> primary frequencies:  these are a DC component and two 
> separate frequencies.  I can calculate the RMS of the 
> composite signal with a bit of integration and the use of 
> the RMS defintion.
> 
> The FFT routine identifies the equivalent power at the 
> discrete frequencies with the Matlab FFT algorithm.  I am 
> plotting the frequency vs. the FFT * the conjugate of the 
> FFT to obtain the power signal.  For the n point data 
> acquisition, I am doing the following to obtain the power:
> 
> Y = fft(v,n);
> 
> Pyy = Y.*conj(Y)/n ;
> 
> Does someone out there know how to extract the equivalent 
> RMS components of the other frequency content?
> 
> best regards
> 
> J. Costello
> 
> 
Its late on Friday afternoon, so don't expect too much.

Each component in the FFT spectrum represents (once you 
have taken into account any scaling caused by the FFT 
algorithm itself) the amplitude of the complex sinewave 
component. From memory there is a well known relationship 
between the amplitude and RMS value of a sine wave - (so 
well known I can't remember it;-) other than to say it 
contains good factors such as square-root of 2. So if you 
compute the amplitude rather than power spectrum I guess 
you can apply this scaling factor to each and every 
component frequency. I guess a simple bit of algebra will 
allow you to scale it so it applies equally well in the 
power domain.

Hope that helps

Dave Robinson