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Text File  |  1996-03-14  |  7KB  |  133 lines
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  4. ccccssssccccaaaallll2222dddd,,,,zzzzssssccccaaaallll2222dddd((((3333FFFF))))                                        ccccssssccccaaaallll2222dddd,,,,zzzzssssccccaaaallll2222dddd((((3333FFFF))))
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  8. NNNNAAAAMMMMEEEE
  9.      ccccssssccccaaaallll2222dddd,,,, zzzzssssccccaaaallll2222dddd ---- scales a 2D complex sequence.
  10.  
  11. SSSSYYYYNNNNOOOOPPPPSSSSYYYYSSSS
  12.      _F_o_r_t_r_a_n :
  13.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee ccccssssccccaaaallll2222dddd(((( nnnn1111,,,, nnnn2222,,,, aaaallllpppphhhhaaaa,,,, aaaarrrrrrrraaaayyyy,,,, llllddddaaaa))))
  14.           iiiinnnntttteeeeggggeeeerrrr     nnnn1111,,,, nnnn2222,,,, llllddddaaaa
  15.           rrrreeeeaaaallll        aaaallllpppphhhhaaaa
  16.           ccccoooommmmpppplllleeeexxxx     aaaarrrrrrrraaaayyyy((((llllddddaaaa,,,,nnnn2222))))
  17.      ssssuuuubbbbrrrroooouuuuttttiiiinnnneeee zzzzssssccccaaaallll2222dddd(((( nnnn1111,,,, nnnn2222,,,, aaaallllpppphhhhaaaa,,,, aaaarrrrrrrraaaayyyy,,,, llllddddaaaa))))
  18.           iiiinnnntttteeeeggggeeeerrrr     nnnn1111,,,, nnnn2222,,,, llllddddaaaa
  19.           rrrreeeeaaaallll****8888      aaaallllpppphhhhaaaa
  20.           ddddoooouuuubbbblllleeee ccccoooommmmpppplllleeeexxxx aaaarrrrrrrraaaayyyy((((llllddddaaaa,,,,nnnn2222))))
  21.  
  22.      _C :
  23.      ####iiiinnnncccclllluuuuddddeeee <<<<fffffffftttt....hhhh>>>>
  24.      iiiinnnntttt ccccssssccccaaaallll2222dddd((((iiiinnnntttt nnnn1111,,,,iiiinnnntttt nnnn2222,,,,ffffllllooooaaaatttt aaaallllpppphhhhaaaa,,,,
  25.                ccccoooommmmpppplllleeeexxxx ****aaaarrrrrrrraaaayyyy,,,,iiiinnnntttt llllddddaaaa))));;;;
  26.      iiiinnnntttt zzzzssssccccaaaallll2222dddd((((iiiinnnntttt nnnn1111,,,,iiiinnnntttt nnnn2222,,,,ddddoooouuuubbbblllleeee aaaallllpppphhhhaaaa,,,,
  27.                zzzzoooommmmpppplllleeeexxxx ****aaaarrrrrrrraaaayyyy,,,,iiiinnnntttt llllddddaaaa))));;;;
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  30. DDDDEEEESSSSCCCCRRRRIIIIPPPPTTTTIIIIOOOONNNN
  31.      ccccssssccccaaaallll2222dddd and zzzzssssccccaaaallll2222dddd scale a 2D complex sequence of size N1xN2.
  32.      The Fourier Transforms are not normalized so the succession Direct-
  33.      Inverse transform scales the input data by a factor equal to the size of
  34.      the transform.  So ccccssssccccaaaallll2222dddd or zzzzssssccccaaaallll2222dddd may be used to scale back the
  35.      result.
  36.  
  37. PPPPAAAARRRRAAAAMMMMEEEETTTTEEEERRRRSSSS
  38.      NNNN1111 ---- Integer, the first dimension size of the 2D sequence.
  39.      Unchanged on exit.
  40.  
  41.      NNNN2222 ---- Integer, the second dimension size of the 2D sequence.
  42.      Unchanged on exit.
  43.  
  44.      AAAAllllpppphhhhaaaa ---- scaling floating point value.
  45.  
  46.      AAAARRRRRRRRAAAAYYYY ---- Array containing the samples of the 2D sequence to be
  47.      transformed.
  48.      On input, the element {i,j} of the sequence is stored as A(i,j) in
  49.      _F_o_r_t_r_a_n , and A[i+j*lda] in _C.
  50.      On exit, the array is overwritten by its transform.  LLLLDDDDAAAA ---- Integer,
  51.      leading dimension: increment between the samples of two consecutive sub-
  52.      sequences (e.g between {i,j+1} and {i,j}).
  53.      Unchanged on exit.
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  55.  
  56. EEEExxxxaaaammmmpppplllleeee ooooffff CCCCaaaalllllllliiiinnnngggg SSSSeeeeqqqquuuueeeennnncccceeee
  57.      Given a 2D complex sequence of size 64x1024.  We successively apply a
  58.      Direct Fourier Transform, an Inverse Fourier Transform and finally scale
  59.      back the result by a factor 1/N (1/(64*1024.))-
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  63.                                                                         PPPPaaaaggggeeee 1111
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  70. ccccssssccccaaaallll2222dddd,,,,zzzzssssccccaaaallll2222dddd((((3333FFFF))))                                        ccccssssccccaaaallll2222dddd,,,,zzzzssssccccaaaallll2222dddd((((3333FFFF))))
  71.  
  72.  
  73.  
  74.      This succession DirectFFT-InverseFFT-Scaling is equivalent to the
  75.      identity operator and the final sequence should be equal (with round-off
  76.      precision) to the initial sequence.
  77.      The offset between the first element of two succesive sub-sequence
  78.      (leading dimension) is 2049.
  79.      _F_o_r_t_r_a_n
  80.           complex array(0:2049-1,0:64-1), coeff(1024+64+2*15)
  81.           call cfft2di( 1024, coeff)
  82.           call cfft2d( -1, 1024, 64, array, 2049, coeff)
  83.           call cfft2d(  1, 1024, 64, array, 2049, coeff)
  84.           call cscal2d(1024,64,(1./real(1024*64)),array,2049)
  85.  
  86.      _C
  87.           #include <fft.h>
  88.           complex array[64*2049], *coeff;
  89.           coeff = cfft2di( 1024, NULL);
  90.           cfft2d( -1, 1024, 64, array, 2049, coeff);
  91.           cfft2d(  1, 1024, 64, array, 2049, coeff);
  92.           cscal2d( 1024,64,1./(float)(1024*64),array,2049);
  93.  
  94.      NNNNOOOOTTTTEEEE____1111 :::: The Direct and Inverse transforms should use opposite signs -
  95.      Which one is used (+1 or -1) for Direct transform is just a matter of
  96.      convention-
  97.  
  98.      NNNNOOOOTTTTEEEE____2222 :::: The Fourier Transforms are not normalized so the succession
  99.      Direct-Inverse transform scales the input data by a factor equal to the
  100.      size of the transform.
  101.  
  102. SSSSEEEEEEEE AAAALLLLSSSSOOOO
  103.      fft, cfft2di, zfft2di, cfft2d, zfft2d, cprod2d, zprod2d
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  129.                                                                         PPPPaaaaggggeeee 2222
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