Skip to content Skip to navigation

Connexions

You are here: Home » Content » Program 10: Split-Radix, DIF, One-Butterfly, FFT

Navigation

Content Actions

  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the author

Recently Viewed

This feature requires Javascript to be enabled.

Program 10: Split-Radix, DIF, One-Butterfly, FFT

Module by: C. Sidney Burrus

Summary: Split-Radix, DIF, One-Butterfly, FFT

Basic DIF Split Radix FFT Algorithm

Below is the Fortran code for a simple Decimation-in-Frequency, Split-Radix, one butterfly FFT to be followed by a bit-reversing unscrambler.

C   A DUHAMEL-HOLLMANN SPLIT RADIX  FFT PROGRAM
C   FROM: ELECTRONICS LETTERS, JAN. 5, 1984
C   COMPLEX INPUT DATA IN ARRAYS X AND Y
C   LENGTH IS  N = 2 ** M
C     C. S. BURRUS, RICE UNIVERSITY, MARCH 1984
C
C---------------------------------------------------------
    SUBROUTINE  FFT (X,Y,N,M)
    REAL X(1), Y(1)
C--------------MAIN FFT LOOPS-----------------------------
C
    N1 = N
    N2 = N/2
    IP = 0
    IS = 1
    A  = 6.283185307179586/N
    DO 10 K = 1, M-1
        JD = N1 + N2
        N1 = N2
        N2 = N2/2
        J0 = N1*IP + 1
        IP = 1 - IP
        DO 20 J = J0, N, JD
            JS = 0
        JT = J + N2 - 1
            DO 30 I = J, JT
            JSS= JS*IS
            JS = JS + 1
                C1 = COS(A*JSS)
                C3 = COS(3*A*JSS)
                S1 = -SIN(A*JSS)
                S3 = -SIN(3*A*JSS)
            I1 = I  + N2
            I2 = I1 + N2
            I3 = I2 + N2
            R1    = X(I ) + X(I2)
            R2    = X(I ) - X(I2)
            R3    = X(I1) - X(I3)
            X(I2) = X(I1) + X(I3)
            X(I1) = R1
C
            R1    = Y(I ) + Y(I2)
            R4    = Y(I ) - Y(I2)
            R5    = Y(I1) - Y(I3)
            Y(I2) = Y(I1) + Y(I3)
            Y(I1) = R1
C
            R1    = R2 - R5
            R2    = R2 + R5
            R5    = R4 + R3
            R4    = R4 - R3
C
            X(I)  = C1*R1 + S1*R5
            Y(I)  = C1*R5 - S1*R1
            X(I3) = C3*R2 + S3*R4
            Y(I3) = C3*R4 - S3*R2
  30            CONTINUE
  20        CONTINUE
        IS = IS + IS
  10    CONTINUE
    IP = 1 - IP
    J0 = 2 - IP
    DO 5 I = J0, N-1, 3
       I1 = I + 1
       R1    = X(I) + X(I1)
       X(I1) = X(I) - X(I1)
       X(I)  = R1
       R1    = Y(I) + Y(I1)
       Y(I1) = Y(I) - Y(I1)
       Y(I)  = R1
   5    CONTINUE
    RETURN
    END

References

    Comments, questions, feedback, criticisms?

    Send feedback