Re:[ncl-talk] 1D fft and spectra

I neglected to post the sample plots. See:
   
   http://www.cgd.ucar.edu/~shea/1DfftExmpl.png

Also, for the record, the units returned by specx_anal:

   (units_of_variable)^2 / frequency_interval

---
On Sun, 27 May 2007, Dennis Shea wrote:
> I responded to Verica. Perhaps I did not post to ncl-talk.
> 
> I have attached a script. It clearly demonstrates that
> 
> [1] The shape of the periodograms calculated via ezfftf and
>     specx_anal are the same. If you want the ezfftf periodogram
>     estimates to have the same scale, multiply the
>     values by (N/2).
>            ;spcfft = spcfft*(nw/2) ; normalize
> 
> [2] The scales are different. As noted in the documentation,
>     the specx_anal periodogram has been normalized so that
>     the area under the curve is the same as the population
>     variance of the input data.
> 
> [3] The attached script explicitly calculates the area.
>     The variance matches the input series.
> 
> 
> Cheers!
> 
> 
> 
> 
> On Mon, 28 May 2007, xiexin163_at_zju.edu.cn wrote:
> 
> > 
> > Hi,
> > 
> > I have the same problem as Verica has when I use these two functions
> > to calculate some power spectra(raw periodogram). However, I also got
> > different anwsers. Following the description on the specx_anal site, I know
> > that what specx_anal is trying to do is first calculate the fourier
> > coefficients of sine and cosine. Then it calculate each (ak^2+bk^2)/2.
> > That is periodogram.
> > 
> > To prove that, I use ezfftf to do the same thing as the above but got
> > anwsers different from what specx_anal gives. The result from specx_anal
> > is quite larger than what ezfftf gives. Thought not totally the same, the
> > plot shape is quite similar. I do not know whether the definitions of
> > these two are the same. Anyone can explain that?
> > 
> > Your help is appreciated!
> > 
> > Xie Xin
> > 
> > > Hi All,
> > > 
> > > I have a question regarding the 1D fft and 1D spectra, in respect to  
> > > the very different results for the spectra constructed using ezfftf  
> > > comparing to the spectra from specx_anal.
> > > Attached is the plot with the resulting curves. On the left hand side  
> > > is specx_anal curve, and on the right hand side is the curve from  
> > > ezfftf.
> > > In addition to very different shape of the curve and very different  
> > > values on the Y axis, I have also found a mismatch between the  
> > > variances calculated from the two spectra. From the description of  
> > > the specx_anal, area under the curve should give the total variance  
> > > of the initial v
> > > ariable. I've tried comparing the variance with the area under the  
> > > curve from ezfftf and curve from specx_anal and I get about 5 times  
> > > larger value for the integral under specx_anal:
> > > integral(spectra from ezfftf) = 0.291434
> > > variance(data) = 0.292072
> > > xvari = 0.291501
> > > xvaro = 0.291501
> > > integral(spectra from specx_anal) = 1.71725
> > > xvari and xvaro are the attributes of the result of specx_anal.
> > > 
> > > In addition to the plot, I've also attached the code with both  
> > > routines and a file with sample of data I used for this example.
> > > 
> > > Does someone know what is the difference?
> > > 
> > > Thank you,
> > > Verica
> > 
> > 
> > _______________________________________________
> > ncl-talk mailing list
> > ncl-talk_at_ucar.edu
> > http://mailman.ucar.edu/mailman/listinfo/ncl-talk
> > 
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