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

Module by: C. Sidney Burrus. E-mail the author

## 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


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