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From: NZTideMan <mulgor@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: FFT - Output to RMS Equivalents
Date: Sun, 4 May 2008 03:18:34 -0700 (PDT)
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On May 3, 3:03=A0am, "John Costello" <JohnCoste...@ChampAero.com> wrote:
> Dave
>
> Thanks for your update. =A0I 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? =A0Since 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.robin...@somewhere.biz> wrote in
> message <fvf8bn$pb...@fred.mathworks.com>...
>
>
>
> > "John Costello" <JohnCoste...@ChampAero.com> wrote in
> > message <fvf4jm$4d...@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: =A0these are a DC component and two
> > > separate frequencies. =A0I 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. =A0I
> am
> > > plotting the frequency vs. the FFT * the conjugate of
> the
> > > FFT to obtain the power signal. =A0For the n point data
> > > acquisition, I am doing the following to obtain the
> power:
>
> > > Y =3D fft(v,n);
>
> > > Pyy =3D 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- Hide quoted text -
>
> - Show quoted text -


A clue:
The RMS value includes the DC or mean, whereas the amplitudes from the
FFT exclude the mean ( it is in the zeroth frequency bin).