Skip to content Skip to navigation

Connexions

You are here: Home » Content » Program 11: Split-Radix, DIF, Two-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.

      What are tags? tag icon

      Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

    • External bookmarks
  • E-mail the author
  • Rate this module (How does the rating system work?)

    Rating system

    Ratings

    Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

    How to rate a module

    Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

    		(0 ratings)

Recently Viewed

This feature requires Javascript to be enabled.

Program 11: Split-Radix, DIF, Two-Butterfly, FFT

Module by: C. Sidney Burrus

Summary: Very efficient Split-Radix DIF, Two Butterfly FFT

DIF Split Radix FFT Algorithm

Below is the Fortran code for a simple Decimation-in-Frequency, Split-Radix, two butterfly FFT to be followed by a bit-reversing unscrambler. Twiddle factors are precalculated and stored in arrays WR and WI.

C--------------------------------------------------------------C
C       A DUHAMEL-HOLLMAN SPLIT RADIX FFT                      C
C       REF: ELECTRONICS LETTERS, JAN. 5, 1984                 C
C       COMPLEX INPUT AND OUTPUT DATA IN ARRAYS X AND Y        C
C       LENGTH IS N = 2 ** M,  OUTPUT IN BIT-REVERSED ORDER    C
C   TWO BUTTERFLIES TO REMOVE MULTS BY UNITY               C
C       SPECIAL LAST TWO STAGES                                C
C   TABLE LOOK-UP OF SINE AND COSINE VALUES            C
C       C.S. BURRUS,       RICE UNIV.       APRIL 1985         C
C--------------------------------------------------------------C
C
        SUBROUTINE FFT(X,Y,N,M,WR,WI)
        REAL X(1),Y(1),WR(1),WI(1)
    C81= 0.707106778
        N2 = 2*N
        DO  10 K = 1, M-3
        IS  = 1
        ID  = N2
        N2 = N2/2
        N4 = N2/4
 2      DO 1 I0 = IS, N-1, ID
        I1 = I0 + N4
        I2 = I1 + N4
            I3 = I2 + N4
        R1    = X(I0) - X(I2)
        X(I0) = X(I0) + X(I2)
        R2    = Y(I1) - Y(I3)
        Y(I1) = Y(I1) + Y(I3)
        X(I2) = R1 + R2
        R2    = R1 - R2
        R1    = X(I1) - X(I3)
        X(I1) = X(I1) + X(I3)
            X(I3) = R2
            R2    = Y(I0) - Y(I2)
                Y(I0) = Y(I0) + Y(I2)
            Y(I2) =-R1 + R2
            Y(I3) = R1 + R2
  1     CONTINUE
        IS = 2*ID - N2 + 1
        ID = 4*ID
            IF (IS.LT.N) GOTO 2
        IE  = N/N2
            IA1 = 1
            DO  20 J = 2, N4
                IA1 = IA1 + IE
                IA3 = 3*IA1 - 2
                CC1 = WR(IA1)
                SS1 = WI(IA1)
                CC3 = WR(IA3)
                SS3 = WI(IA3)
                IS  = J
                ID  = 2*N2
 40             DO 30 I0 = IS, N-1, ID
                    I1 = I0 + N4
                    I2 = I1 + N4
                    I3 = I2 + N4
C
                    R1    = X(I0) - X(I2)
                    X(I0) = X(I0) + X(I2)
                    R2    = X(I1) - X(I3)
                    X(I1) = X(I1) + X(I3)
                    S1    = Y(I0) - Y(I2)
                    Y(I0) = Y(I0) + Y(I2)
                    S2    = Y(I1) - Y(I3)
                    Y(I1) = Y(I1) + Y(I3)
C
                    S3    = R1 - S2
                    R1    = R1 + S2
                    S2    = R2 - S1
                    R2    = R2 + S1
                    X(I2) = R1*CC1 - S2*SS1
                    Y(I2) =-S2*CC1 - R1*SS1
                    X(I3) = S3*CC3 + R2*SS3
                    Y(I3) = R2*CC3 - S3*SS3
 30             CONTINUE
                IS = 2*ID - N2 + J
                ID = 4*ID
                IF (IS.LT.N) GOTO 40
  20        CONTINUE
  10    CONTINUE
C
        IS =  1
        ID = 32
  50    DO 60 I = IS, N, ID
            I0    = I + 8
            DO 15 J = 1, 2
               R1 = X(I0)   + X(I0+2)
               R3 = X(I0)   - X(I0+2)
               R2 = X(I0+1) + X(I0+3)
               R4 = X(I0+1) - X(I0+3)
               X(I0)   = R1 + R2
               X(I0+1) = R1 - R2
               R1 = Y(I0)   + Y(I0+2)
               S3 = Y(I0)   - Y(I0+2)
               R2 = Y(I0+1) + Y(I0+3)
               S4 = Y(I0+1) - Y(I0+3)
               Y(I0)   = R1 + R2
               Y(I0+1) = R1 - R2
               Y(I0+2) = S3 - R4
               Y(I0+3) = S3 + R4
               X(I0+2) = R3 + S4
               X(I0+3) = R3 - S4
               I0 = I0 + 4
  15        CONTINUE
  60    CONTINUE
            IS = 2*ID - 15
            ID = 4*ID
        IF (IS.LT.N) GOTO 50
C
        IS =  1
        ID = 16
  55    DO 65 I0 = IS, N, ID
                R1 = X(I0)   + X(I0+4)
            R5 = X(I0)   - X(I0+4)
            R2 = X(I0+1) + X(I0+5)
            R6 = X(I0+1) - X(I0+5)
            R3 = X(I0+2) + X(I0+6)
            R7 = X(I0+2) - X(I0+6)
            R4 = X(I0+3) + X(I0+7)
            R8 = X(I0+3) - X(I0+7)
            T1 = R1 - R3
            R1 = R1 + R3
            R3 = R2 - R4
            R2 = R2 + R4
            X(I0)   = R1 + R2
            X(I0+1) = R1 - R2
C
            R1 = Y(I0)   + Y(I0+4)
            S5 = Y(I0)   - Y(I0+4)
            R2 = Y(I0+1) + Y(I0+5)
            S6 = Y(I0+1) - Y(I0+5)
            S3 = Y(I0+2) + Y(I0+6)
            S7 = Y(I0+2) - Y(I0+6)
            R4 = Y(I0+3) + Y(I0+7)
            S8 = Y(I0+3) - Y(I0+7)
            T2 = R1 - S3
            R1 = R1 + S3
            S3 = R2 - R4
            R2 = R2 + R4
            Y(I0)   = R1 + R2
            Y(I0+1) = R1 - R2
            X(I0+2) = T1 + S3
            X(I0+3) = T1 - S3
            Y(I0+2) = T2 - R3
            Y(I0+3) = T2 + R3
C
            R1 = (R6 - R8)*C81
            R6 = (R6 + R8)*C81
            R2 = (S6 - S8)*C81
            S6 = (S6 + S8)*C81
C
            T1 = R5 - R1
            R5 = R5 + R1
            R8 = R7 - R6
            R7 = R7 + R6
            T2 = S5 - R2
            S5 = S5 + R2
            S8 = S7 - S6
            S7 = S7 + S6
            X(I0+4) = R5 + S7
            X(I0+7) = R5 - S7
            X(I0+5) = T1 + S8
            X(I0+6) = T1 - S8
            Y(I0+4) = S5 - R7
            Y(I0+7) = S5 + R7
            Y(I0+5) = T2 - R8
            Y(I0+6) = T2 + R8
  65    CONTINUE
            IS = 2*ID - 7
            ID = 4*ID
        IF (IS.LT.N) GOTO 55
C
C------------BIT REVERSE COUNTER-----------------
C
  100   J = 1
        N1 = N - 1
        DO 104 I=1, N1
            IF (I.GE.J) GOTO 101
            XT = X(J)
            X(J) = X(I)
            X(I) = XT
            XT   = Y(J)
            Y(J) = Y(I)
            Y(I) = XT
  101       K = N/2
  102       IF (K.GE.J) GOTO 103
                J = J - K
                K = K/2
                GOTO 102
  103       J = J + K
  104   CONTINUE
        RETURN
        END

References

    Comments, questions, feedback, criticisms?

    Send feedback