fft different results by ezzfft and cfft

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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Received on Mon Mar 22 09:53:22 2010