| Complications with variance using FFTs [message #40166] |
Fri, 16 July 2004 11:08 |
olde_english33
Messages: 7
Registered: June 2004
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Junior Member |
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First I computed the FFT of a recorded time series. I then computed
the spectrum of this time series to keep the amplitudes of the
original data. I then wanted to tie in a random phase because I want
to give variables the same kind of shape when I inverse transform.
Here is a sample of my code:
for i=0,12 do begin
Xf1[*,i]=fft(xf1[*,i])*31.0
Xf2[*,i]=fft(xf2[*,i])*31.0
specx1[*,i]=Xf1[*,i]*conj(Xf1[*,i])/31.0
specx2[*,i]=Xf2[*,i]*conj(Xf2[*,i])/31.0
endfor
for i=0,30 do begin
avgspec1=mean(spec1[i,*])
avgspec2=mean(spec2[i,*])
endfor
for j=0,99 do begin
ggg=randomu(5*j*!PI,15)
hhh[0]=0.0
hhh[1:15]=ggg
for k=0,14 do begin
hhh[30-k]=ggg[k]
endfor
aaa[*,j]=(randomu(2*j+3,31)-0.5)*sqrt(12.0)
bbb[*,j]=fft(aaa[*,j])
ccc1[*,j]=bbb[*,j]*exp(2.0*!PI*hhh*imag)
ccc2[*,j]=bbb[*,j]*exp(2.0*!PI*hhh*imag)
ddd1[*,j]=(fft(ccc1[*,j],1))
ddd2[*,j]=(fft(ccc2[*,j],1))
endfor
My dilemma is that the average sample variances of the generated time
series ddd1 and ddd2 are nowhere close to the average sample variance
of the orginal time series xf1 and xf2. A colleague and I have
narrowed it down to the fact that we are multiplying the spectrum by a
random phase which is throwing off the variance but I don't know how
to counteract this problem. Can anyone help???
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