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SUBROUTINE DE01OD( CONV, N, A, B, INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute the convolution or deconvolution of two real signals
C A and B.
C
C ARGUMENTS
C
C Mode Parameters
C
C CONV CHARACTER*1
C Indicates whether convolution or deconvolution is to be
C performed as follows:
C = 'C': Convolution;
C = 'D': Deconvolution.
C
C Input/Output Parameters
C
C N (input) INTEGER
C The number of samples. N must be a power of 2. N >= 2.
C
C A (input/output) DOUBLE PRECISION array, dimension (N)
C On entry, this array must contain the first signal.
C On exit, this array contains the convolution (if
C CONV = 'C') or deconvolution (if CONV = 'D') of the two
C signals.
C
C B (input) DOUBLE PRECISION array, dimension (N)
C On entry, this array must contain the second signal.
C NOTE that this array is overwritten.
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C This routine computes the convolution or deconvolution of two real
C signals A and B using an FFT algorithm (SLICOT Library routine
C DG01MD).
C
C REFERENCES
C
C [1] Rabiner, L.R. and Rader, C.M.
C Digital Signal Processing.
C IEEE Press, 1972.
C
C NUMERICAL ASPECTS
C
C The algorithm requires 0( N*log(N) ) operations.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1997.
C Supersedes Release 2.0 routine DE01CD by R. Dekeyser, State
C University of Gent, Belgium.
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Convolution, deconvolution, digital signal processing, fast
C Fourier transform, real signals.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0D0, HALF=0.5D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
CHARACTER CONV
INTEGER INFO, N
C .. Array Arguments ..
DOUBLE PRECISION A(*), B(*)
C .. Local Scalars ..
LOGICAL LCONV
INTEGER J, KJ, ND2P1
DOUBLE PRECISION AC, AS, AST, BC, BS, CI, CR
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DG01MD, DLADIV, DSCAL, XERBLA
C .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MOD
C .. Executable Statements ..
C
INFO = 0
LCONV = LSAME( CONV, 'C' )
C
C Test the input scalar arguments.
C
IF( .NOT.LCONV .AND. .NOT.LSAME( CONV, 'D' ) ) THEN
INFO = -1
ELSE
J = 0
IF( N.GE.2 ) THEN
J = N
C WHILE ( MOD( J, 2 ).EQ.0 ) DO
10 CONTINUE
IF ( MOD( J, 2 ).EQ.0 ) THEN
J = J/2
GO TO 10
END IF
C END WHILE 10
END IF
IF ( J.NE.1 ) INFO = -2
END IF
C
IF ( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'DE01OD', -INFO )
RETURN
END IF
C
C Fourier transform.
C
CALL DG01MD( 'Direct', N, A, B, INFO )
C
IF ( LCONV ) THEN
AST = A(1)*B(1)
ELSE
IF ( B(1).EQ.ZERO ) THEN
AST = ZERO
ELSE
AST = A(1)/B(1)
END IF
END IF
C
ND2P1 = N/2 + 1
J = ND2P1
C
DO 20 KJ = ND2P1, N
C
C Components of the transform of function A.
C
AC = HALF*( A(J) + A(KJ) )
AS = HALF*( B(J) - B(KJ) )
C
C Components of the transform of function B.
C
BC = HALF*( B(KJ) + B(J) )
BS = HALF*( A(KJ) - A(J) )
C
C Deconvolution by complex division if CONV = 'D';
C Convolution by complex multiplication if CONV = 'C'.
C
IF ( LCONV ) THEN
CR = AC*BC - AS*BS
CI = AS*BC + AC*BS
ELSE
IF ( MAX( ABS( BC ), ABS( BS ) ).EQ.ZERO ) THEN
CR = ZERO
CI = ZERO
ELSE
CALL DLADIV( AC, AS, BC, BS, CR, CI )
END IF
END IF
C
A(J) = CR
B(J) = CI
A(KJ) = CR
B(KJ) = -CI
J = J - 1
20 CONTINUE
A(1) = AST
B(1) = ZERO
C
C Inverse Fourier transform.
C
CALL DG01MD( 'Inverse', N, A, B, INFO )
C
CALL DSCAL( N, ONE/DBLE( N ), A, 1 )
C
RETURN
C *** Last line of DE01OD ***
END
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