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c
c-----------------------------------------------------------------------
c subroutine: iftohm
c compute idft 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 iftohm(x, n)
dimension x(1)
c
c x = real array which on input contains the n/4 complex values of the
c odd harmonics of the input--stored in the sequence re(x(1)),
c im(x(1)),re(x(2)),im(x(2)),...
c on output x contains the first n/2 points of the input
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 idft directly
c
if (n.gt.2) go to 10
x(1) = 0.5*x(1)
x(2) = -x(1)
return
10 twopi = 8.*atan(1.0)
tpn = twopi/float(n)
no2 = n/2
no4 = n/4
nind = no2
c
c solve for x(0)=x0 directly
c
x0 = 0.
do 20 i=1,no2,2
x0 = x0 + 2.*x(i)
20 continue
x0 = x0/float(n)
c
c form y(k)=j*(x(2k+1)-x(2k-1))
c overwrite x array with y sequence
c
xpr = x(1)
xpi = x(2)
x(1) = -2.*x(2)
x(2) = 0.
if (no4.eq.1) go to 40
do 30 i=3,nind,2
ti = x(i) - xpr
tr = -x(i+1) + xpi
xpr = x(i)
xpi = x(i+1)
x(i) = tr
x(i+1) = ti
30 continue
40 x(no2+1) = 2.*xpi
x(no2+2) = 0.
c
c take n/2 point (real) ifft of preprocessed sequence x
c
call fsst(x, no2)
c
c solve for x(m) by dividing by 4*sin(twopi*m/n) for m=1,2,...,n/2-1
c for m=0 substitute precomputed value x0
c
cosi = 4.
sini = 0.
cosd = cos(tpn)
sind = sin(tpn)
do 50 i=2,no2
temp = cosi*cosd - sini*sind
sini = cosi*sind + sini*cosd
cosi = temp
x(i) = x(i)/sini
50 continue
x(1) = x0
return
end
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