Geology Reference
In-Depth Information
The forward and backward prediction error sequences are
F
j
+
N
+
1,
N
+
1
=
f
j
+
N
+
1
+
γ
1,
N
+
1
f
j
+
N
+···+
γ
N
+
1,
N
+
1
f
j
F
j
+
N
+
1,
N
B
=
+
γ
N
+
1,
N
+
1
j
,
N
,
(2.502)
j
,
N
=
f
j
+
γ
∗
1,
N
+
1
f
j
+
1
+···+
γ
∗
N
+
1,
N
+
1
f
j
+
N
+
1
=
+
1
B
j
,
N
+
γ
∗
N
+
1,
N
+
1
F
j
+
N
+
1,
N
,
(2.503)
for
j
=
1,...,
M
−
N
−
1. The prediction error filter coe
cients are updated
according to
+
γ
N
+
1,
N
+
1
γ
∗
N
,
N
,
γ
1,
N
+
1
=
γ
1,
N
+
γ
N
+
1,
N
+
1
γ
∗
N
−
1,
N
,
.
.
.
γ
2,
N
+
1
=
γ
2,
N
=
γ
N
,
N
+
γ
N
+
1,
N
+
1
γ
∗
1,
N
.
γ
N
,
N
+
1
(2.504)
The new autocorrelation is found from
N
+
1
φ
ff
(
N
+
1)
=−
1
γ
j
,
N
+
1
φ
ff
(
N
−
j
+
1),
(2.505)
j
=
and the new prediction error power is found from the recursion
P
N
+
1
1
−
γ
N
+
1,
N
+
1
γ
∗
N
+
1,
N
+
1
.
=
P
N
+
2
(2.506)
The subroutine BPEC performs the recursion to find the prediction error coef-
ficients G of length NP1 from those of length N for the given data sequence F
of length M. Current values of the prediction error coe
cients, and the forward
and backward prediction error sequences, are included as input and their updated
values are returned as output.
SUBROUTINE BPEC(M,NP1,F,G,PEF,PER)
C
C Subroutine BPEC finds the prediction error filter coefficients G
C of length NP1 from those of length N for the time sequence F of length M.
C It also returns the forward and backward prediction error sequences.
C
IMPLICIT DOUBLE COMPLEX (A-H,O-Z)
DIMENSION F(M),G(M),H(M),O(M),PEF(M),PER(M)
C Find previous recursion number.
N=NP1-1
IF(N.NE.0) GO TO 10
C If previous recursion number is zero, set forward and backward
C prediction error sequences to given data sequence.
DO 11 J=1,M
PEF(J)=F(J)
PER(J)=F(J)
11
CONTINUE
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