SUBROUTINE WFT(NUM,X)
C
C	THIS COMPUTES THE FAST WALSH-FOURIER TRANSFORM
C	  IN SEQUENCY ORDER (ref: Ahmed & Rao 1975)
c
c       The data X are a univariate series of length NUM
C
c	NUM is 2^power, max is 2^15=32768
c		but this can be adjusted in IPOWER
c
c	The data X are returned as the Walsh-Fourier transform
c              in sequency order
C	 
C
C
	REAL X(32768),Y(32768)
	INTEGER IPOWER(15)
C
C
	DO 11 I=1,NUM
	IB=I-1
	IL=1
9	IBD=IB/2
	IPOWER(IL)=1
	IF (IB .EQ. (IBD*2)) IPOWER(IL)=0
        IF (IB .EQ. 0) GO TO 10
	IB=IBD
	IL=IL+1
	GO TO 9
10	CONTINUE
	IP=1
	IFAC=NUM
	DO 12 I1=1,IL
	IFAC=IFAC/2
12	IP=IP+IFAC*IPOWER(I1)
11	Y(IP)=X(I)
	DO 13 I=1,NUM
13	X(I)=Y(I)
C
65	ITER=0
	IREM=NUM
1	IREM=IREM/2
	IF (IREM .EQ. 0) GO TO 2
	ITER=ITER+1
	GO TO 1
2	CONTINUE
C
	DO 50 M=1,ITER
	IF (M .EQ. 1) NUMP=1
	IF (M .NE. 1) NUMP=NUMP*2
	MNUM=NUM/NUMP
	MNUM2=MNUM/2
C
	ALPH=1.0
	DO 49 MP=1,NUMP
	IB=(MP-1)*MNUM
C
	DO 48 MP2=1,MNUM2
	MNUM21=MNUM2+MP2+IB
	IBA=IB+MP2
	Y(IBA)=X(IBA)+ALPH*X(MNUM21)
	Y(MNUM21)=X(IBA)-ALPH*X(MNUM21)
48	CONTINUE
	ALPH=-ALPH
49	CONTINUE
C
	r=1.0/sqrt(float(num))
	DO 7 I=1,NUM
7	X(I)=Y(I)*r
50	CONTINUE
	RETURN
	END