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From: "John Costello" <JohnCostello@ChampAero.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT - Output to RMS Equivalents
Date: Fri, 2 May 2008 15:03:03 +0000 (UTC)
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Dave

Thanks for your update.  I am aware of the sqrt(2) 
equivalence for a simple sinusoid with an RMS equivalent...

what I am wrestling with at the moment is...

a composite signal with a dc offset, and two extra (could 
be more) sinuodal frequencies modulated (or superimposed) 
on the dc carrier....

The output of the FFT algorithm produces a discrete number 
of complex numbers corresponding to x + iy for each 
frequency...

The product of x + iy times its conjugate x - iy yields the 
absolute value or magnitude squared....

so, when plotted as power (or the signal FFT squared)... 
against frequency, I obtain a plot of a squared term vs. 
frequency...

For argument sake suppose the power coefficient of the 
first major term in the plot occurs at 100 Hz and has an 
amplitude of 10, the second major term occurs at 1 KHz and 
has an amplitude of 5....

Is there a simple mechanism for exracting the RMS 
equivalents for the 100 Hz and 1 KHz content, equivalent 
amplitude of the RMS signal for each of the discrete 
frequencies?  Since I'm working with a squared relationship 
between power (squared term) back to equivalent amplitude 
of a voltage waveform for either 100 Hz or 1 KHz...

Thanks for your input on this issue.

cheers

John Costello

"Dave Robinson" <dave.robinson@somewhere.biz> wrote in 
message <fvf8bn$pb9$1@fred.mathworks.com>...
> "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