Re: fft different results by ezzfft and cfft

I think the documentation covers this. See the "Description" section
and Example 1.

==
The cfftf function returns the same information as the forward real
discrete fourier transform, ezfftf. The returned information is in a
different form, in particular, the representation of frequency. The real
forward transform pertains to the positive frequency portion of the
spectrum while the complex forward transform includes positive and
negative frequencies. The following is a slightly edited excerpt from
the Smith reference.
[snip] ...

Also, see:
http://www.ncl.ucar.edu/Document/Functions/Built-in/cfftf_frq_reorder.shtml

This further explains some information.

===

Which to use ... it depends on what it is
you want to do:
traveling waves ... cfftf
power ... ezfft

Good luck

On 03/22/2010 09:56 AM, Sergio Abarca wrote:
>
> Hi all,
>
> I am doing a fft and I am puzzled about the output of ezzfft and cfftf.
> I use the NCL example (given in the ezfft function) of a sequence "x"
> (below) and do the fourier transform using both ezzfft and cfftf. When
> using cfftf I add an imaginary part =0. The coefficients differ from
> each other by a factor of N (the number of elements in the "x" array, in
> this case 24), for the wave number "0" coefficient and a factor of N/2,
> for the rest of the coefficients.
>
> Any idea of why? And, which one should I use? I got into this because in
> using ezzfft the difference in magnitude between wavenumber 0 and
> wavenumber 1 in the (hurricane) data I am using seemed abnormally high,
> between 2 and 3 orders of magnitude, when I expected it to be between a
> factor of 2 and an order of magnitude.
>
> Thanks,
> Sergio
>
>
> load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_code.ncl"
> begin
> x = (/ 1002, 1017, 1018, 1020, 1018, 1027, \
> 1028, 1030, 1012, 1012, 982, 1012, \
> 1001, 996, 995, 1011, 1027, 1025, \
> 1030, 1016, 996, 1006, 1002, 982 /)
> cfReal = ezfftf (x)
> cfComplex = cfftf (x,0,0)
> print(cfReal)
> print(cfComplex)
> end
>
>
> Here is the output:
>
> Variable: cfReal
> Type: float
> Total Size: 96 bytes
> 24 values
> Number of Dimensions: 2
> Dimensions and sizes: [2] x [12]
> Coordinates:
> Number Of Attributes: 2
> npts : 24
> xbar : 1011.042
> (0,0) 1.338438
> (0,1) -13.48403
> (0,2) 2.166667
> (0,3) 3.291667
> (0,4) -5.398408
> (0,5) 0.08333334
> (0,6) -2.724774
> (0,7) 2.708333
> (0,8) 2.166667
> (0,9) -0.3493074
> (0,10) 2.951411
> (0,11) -1.791667
> (1,0) 3.73528
> (1,1) 6.88814
> (1,2) 3.362945
> (1,3) 0.3608439
> (1,4) 3.019545
> (1,5) 1
> (1,6) 4.113242
> (1,7) 1.515544
> (1,8) 2.529612
> (1,9) -2.63814
> (1,10) 2.808251
> (1,11) 0
>
>
> Variable: cfComplex
> Type: float
> Total Size: 192 bytes
> 48 values
> Number of Dimensions: 2
> Dimensions and sizes: [2] x [24]
> Coordinates:
> Number Of Attributes: 2
> npts : 24
> frq : <ARRAY of 24 elements>
> (0,0) 24265
> (0,1) 16.06125
> (0,2) -161.8083
> (0,3) 26
> (0,4) 39.5
> (0,5) -64.78089
> (0,6) 1
> (0,7) -32.69729
> (0,8) 32.5
> (0,9) 26
> (0,10) -4.191688
> (0,11) 35.41693
> (0,12) -43
> (0,13) 35.41693
> (0,14) -4.191688
> (0,15) 26
> (0,16) 32.5
> (0,17) -32.69729
> (0,18) 1
> (0,19) -64.78089
> (0,20) 39.5
> (0,21) 26
> (0,22) -161.8083
> (0,23) 16.06125
> (1,0) 0
> (1,1) -44.82336
> (1,2) -82.65768
> (1,3) -40.35534
> (1,4) -4.330127
> (1,5) -36.23454
> (1,6) -12
> (1,7) -49.3589
> (1,8) -18.18653
> (1,9) -30.35534
> (1,10) 31.65768
> (1,11) -33.69901
> (1,12) 0
> (1,13) 33.69901
> (1,14) -31.65768
> (1,15) 30.35534
> (1,16) 18.18653
> (1,17) 49.3589
> (1,18) 12
> (1,19) 36.23454
> (1,20) 4.330127
> (1,21) 40.35534
> (1,22) 82.65768
> (1,23) 44.82336
>
>
>
>
>
>
>
>
> Sergio Abarca
> Graduate Student
> UCLA Dept of Atmospheric & Oceanic Sciences
> 7127 Math Sciences Building
> 405 Hilgard Avenue
> Los Angeles, CA 90095-1565
> (310) 206.3185
> (310) 206.5219 fax
>
>
>
>
>
>
>
>
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