Geology Reference
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10 IF(I.GE.LGT3M2) GO TO 20
I=I*2
N=N+1
GO TO 10
20 CONTINUE
L=2**N
C Zero fill padded sequences being convolved.
DO 30 I=1,L
WK1(I)=(0.D0,0.D0)
WK2(I)=(0.D0,0.D0)
30 CONTINUE
C Find sequences to be convolved.
DO 40 J=1,LG
JM1=J-1
JM1S=JM1*JM1
ARGJ2=ARG*DFLOAT(JM1S)
DC=DCOS(ARGJ2)
DS=DSIN(ARGJ2)
WK1(J)=FACT*G(J)*DCMPLX(DC,DS)
C Store weights for final DFT calculation.
G(J)=DCMPLX(DC,DS)
JPLGM1=J+LG-1
WK2(JPLGM1)=DCMPLX(DC,-DS)
IF(J.EQ.1) GO TO 40
LGMJP1=LG-J+1
WK2(LGMJP1)=WK2(JPLGM1)
40 CONTINUE
C Find FFTs of sequences entering convolution.
IS=-1
CALL FFT2N(L,WK1,IS)
CALL FFT2N(L,WK2,IS)
C Multiply FFTs to find FFT of convolution.
DO 50 I=1,L
WK1(I)=WK1(I)*WK2(I)
50 CONTINUE
C Find convolution by inverse DFT.
IS=1
CALL FFT2N(L,WK1,IS)
C Weight convolution to obtain DFT.
DO 60 I=1,LG
IPLGM1=I+LG-1
G(I)=G(I)*WK1(IPLGM1)
60
CONTINUE
RETURN
END
2.3.5 The DFT for unequally spaced samples
The description of the discrete Fourier transform (DFT), its properties, and meth-
ods of calculating it, have thus far assumed that the samples in the time domain are
equally spaced. Often, this is not the case. Observations may characteristically be
unequally spaced in, for example, a wide range of astronomical and space meas-
urements, which can only be made at certain times, or when sources are visible.
Another common type of unequally spaced sequence arises when there are gaps in
otherwise equally spaced samples. This may occur when glitches in the signal are
removed, or when the digitiser, or instrument, is subject to failure.
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