From: Wolfgang Langhans <wolfgang.langhans_at_nyahnyahspammersnyahnyah>

Date: Fri Dec 02 2011 - 02:01:21 MST

Date: Fri Dec 02 2011 - 02:01:21 MST

Hi,

I am a bit confused about the outcome of the ezfftf Fourier Forward

analysis. Should not the sum over all squared norms equal the total

biased variance of the data series? How can I understand the different

results obtained in the little example below? How comes that the sum

amounts almost twice the actual variance?

Thanks for your help in understanding this!

Wolfgang

;======================================================

low = -5.0

high = 5.0

con = (high - low) / 32766.0 ; 32766.0 forces a 0.0 to 1.0 range

Z = new(100,float)

do i=0,dimsizes(Z)-1

Z(i) = low + con * rand()

end do

zmean = avg(Z)

zvarbiased = 1./dimsizes(Z) * sum( (Z-zmean)^2 ) ;total biased

variance of original data

zfft = ezfftf(Z)

z = zfft(0,:)^2 + zfft(1,:)^2

nfreq = dimsizes(z)

totvar = sum(z(0:nfreq-1)) ; sum over all squared norms of the

complex Fourier transforms

print("Variance: "+ zvarbiased + " Sum over spectrum: "+totvar )

;======================================================

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Received on Fri Dec 2 02:01:35 2011

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