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CFFT -

D704

: H.H.Umstaetter :

popaa c oo popaoa p oco poco ocoaoc c poo n, , :

d704

poo popaoa,

d704

opaoo popaoa, ak Am - oc ca.
c Am (2) a, op (1), o ak = alfak/n, k=0,1,...,n-1.
oaoo cooa a o o acc coc o o a poo .

:

: - SUBROUTINE
: - CFFT

:

CALL CFFT(A,M), :

A - (COMPLEX*16) acc n.
M - (INTEGER) a o M o oo, opa . coo a op n cooo n=2ABS(M).
c opao, o oc po popaoa (1).
c ooo 0, o - opao (2).
a o c.
<0 : a o A(k+1)=ak, k=0,1,...,n-1.
      a o A(m+1)=Am, a opo (1), m=0,1,...,n-1.
M>=0: a o A(m+1)=Am, m=0,1,...,n-1.
      a o A(k+1)=alfak, a opo (2), k=0,1,...,n-1.

:

o ocoa a aop , (c. [1,2]) c oc oa, oop copaa p ca a a M: o a
exp(im*pi) ac a co a, a a exp(i2*pi/m), m=2,4,...,n, cc ppco c co oo apa op .

:

  1. G.Dahlquist, A.Bjorck, Numrical mthods (Prntic-Hall,
    Englwood Cliffs, 1974), p.416.
  2. L.R.Rabinr, B.Gold, Thor and application of digital signal
    procssing (Prntic-Hall, Englwood Cliffs, 1975), p.332.
:
       . . .
       COMPLEX*16 A(128)
       DO 1 I=1,50
       I1=78+I
       A(I)=(0.D0,0.D0)
    1  A(I1)=(0.D0,0.D0)
       DO 2 I=51,78
    2  A(I)=(1.D0,0.D0)
       CALL CFFT(A,-7)
       . . .
       CALL CFFT(A,7)
       . . .
       DO 3 I=1,128
    3  A(I)=A(I)/128
       . . .
:
             :
 
       A(1)  = (   28.0000,     .0000)   A(50) = (    -.2982,    -.7730)
       A(51) = (     .0698,     .1951)   A(78) = (     .1557,    -.4714)
       A(79) = (     .0698,    -.1951)   A(128)= (  -25.8423,     .6344)
 
         -  :
 
       A(1)  = ( .0000E+00,-.5551E-15)   A(50) = (-.5856E-13, .6682E-13)
       A(51) = ( .1280E+03, .3338E-13)   A(78) = ( .1280E+03,-.3135E-13)
       A(79) = (-.4000E-14,-.3087E-13)   A(128)= (-.8527E-13, .2193E-13)
 
        ,    n=128,   
       (   " "):
 
       A(1)  = ( .0000E+00,-.4337E-17)   A(50) = (-.4575E-15, .5220E-15)
       A(51) = ( .1000E+01, .2608E-15)   A(78) = ( .1000E+01,-.2449E-15)
       A(79) = (-.3125E-16,-.2412E-15)   A(128)= (-.6661E-15, .1713E-15)


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