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c
c-----------------------------------------------------------------------
c subroutine: fftohm
c compute dft for real, n-point, odd harmonic sequences using an
c n/2 point fft
c odd harmonic means x(2*k)=0, all k where x(k) is the dft of x(m)
c note: index m is sequence index--not fortran index
c-----------------------------------------------------------------------
c
subroutine fftohm(x, n)
dimension x(1)
c
c x = real array which on input contains the first n/2 points of the
c input
c on output x contains the n/4 complex values of the odd
c harmonics of the input--stored in the sequence re(x(1)),im(x(1)),
c re(x(2)),im(x(2)),...
c ****note: x must be dimensioned to size n/2+2 for fft routine
c n = true size of x sequence
c
c first compute real(x(1)) and real(x(n/2-1)) separately
c also simultaneously multiply original sequence by sin(twopi*(m-1)/n)
c sin and cos are computed recursively
c
c
c for n = 2, assume x(1)=x0, x(2)=-x0, compute dft directly
c
if (n.gt.2) go to 10
x(1) = 2.*x(1)
x(2) = 0.
return
10 twopi = 8.*atan(1.0)
tpn = twopi/float(n)
c
c compute x1=real(x(1)) and x2=imaginary(x(n/2-1))
c x(n) = x(n)*4.*sin(twopi*(i-1)/n)
c
t1 = 0.
c
c cosd and sind are multipliers for recursion for sin and cos
c cosi and sini are initial conditions for recursion for sin and cos
c
cosd = cos(tpn*2.)
sind = sin(tpn*2.)
cosi = 1.
sini = 0.
no2 = n/2
do 20 i=1,no2,2
t = x(i)*cosi
x(i) = x(i)*4.*sini
temp = cosi*cosd - sini*sind
sini = cosi*sind + sini*cosd
cosi = temp
t1 = t1 + t
20 continue
c
c reset initial conditions (cosi,sini) for new recursion
c
cosi = cos(tpn)
sini = sin(tpn)
t2 = 0.
do 30 i=2,no2,2
t = x(i)*cosi
x(i) = x(i)*4.*sini
temp = cosi*cosd - sini*sind
sini = cosi*sind + sini*cosd
cosi = temp
t2 = t2 + t
30 continue
x1 = 2.*(t1+t2)
x2 = 2.*(t1-t2)
c
c take n/2 point (real) fft of preprocessed sequence x
c
call fast(x, no2)
c
c for n = 4--skip recursion and initial conditions
c
if (n.eq.4) go to 50
c
c initial conditions for recursion
c
x(2) = -x(1)/2.
x(1) = x1
c
c for n = 8, skip recursion
c
if (n.eq.8) go to 50
c
c unscramble y(k) using recursion formula
c
nind = no2 - 2
do 40 i=3,nind,2
t = x(i)
x(i) = x(i-2) + x(i+1)
x(i+1) = x(i-1) - t
40 continue
50 x(no2) = x(no2+1)/2.
x(no2-1) = x2
return
end
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