Purpose
To compute the convolution or deconvolution of two real signals A and B using the Hartley transform.Specification
SUBROUTINE DE01PD( CONV, WGHT, N, A, B, W, INFO )
C .. Scalar Arguments ..
CHARACTER CONV, WGHT
INTEGER INFO, N
C .. Array Arguments ..
DOUBLE PRECISION A(*), B(*), W(*)
Arguments
Mode Parameters
CONV CHARACTER*1
Indicates whether convolution or deconvolution is to be
performed as follows:
= 'C': Convolution;
= 'D': Deconvolution.
WGHT CHARACTER*1
Indicates whether the precomputed weights are available
or not, as follows:
= 'A': available;
= 'N': not available.
Note that if N > 1 and WGHT = 'N' on entry, then WGHT is
set to 'A' on exit.
Input/Output Parameters
N (input) INTEGER
The number of samples. N must be a power of 2. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (N)
On entry, this array must contain the first signal.
On exit, this array contains the convolution (if
CONV = 'C') or deconvolution (if CONV = 'D') of the two
signals.
B (input) DOUBLE PRECISION array, dimension (N)
On entry, this array must contain the second signal.
NOTE that this array is overwritten.
W (input/output) DOUBLE PRECISION array,
dimension (N - LOG2(N))
On entry with WGHT = 'A', this array must contain the long
weight vector computed by a previous call of this routine
or of the SLICOT Library routine DG01OD.f, with the same
value of N. If WGHT = 'N', the contents of this array on
entry is ignored.
On exit, this array contains the long weight vector.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
This routine computes the convolution or deconvolution of two real signals A and B using three scrambled Hartley transforms (SLICOT Library routine DG01OD).References
[1] Van Loan, Charles.
Computational frameworks for the fast Fourier transform.
SIAM, 1992.
Numerical Aspects
The algorithm requires O(N log(N)) floating point operations.Further Comments
NoneExample
Program Text
* DE01PD EXAMPLE PROGRAM TEXT
* Copyright (c) 2002-2017 NICONET e.V.
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER NMAX
PARAMETER ( NMAX = 128 )
* .. Local Scalars ..
INTEGER I, INFO, N
CHARACTER*1 CONV, WGHT
* .. Local Arrays ..
DOUBLE PRECISION A(NMAX), B(NMAX), W(NMAX)
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL DE01PD
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N, CONV, WGHT
IF ( N.LT.0 .OR. N.GT.NMAX ) THEN
WRITE ( NOUT, FMT = 99994 ) N
ELSE
READ ( NIN, FMT = * ) ( A(I), B(I), I = 1,N )
* Perform convolution on A and B.
CALL DE01PD( CONV, WGHT, N, A, B, W, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
IF ( LSAME( CONV, 'C' ) ) THEN
WRITE ( NOUT, FMT = 99997 )
ELSE
WRITE ( NOUT, FMT = 99996 )
END IF
DO 20 I = 1, N
WRITE ( NOUT, FMT = 99995 ) I, A(I)
20 CONTINUE
END IF
END IF
STOP
*
99999 FORMAT (' DE01PD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from DE01PD = ',I2)
99997 FORMAT (' Convolution ',//' i A(i)',/)
99996 FORMAT (' Deconvolution ',//' i A(i)',/)
99995 FORMAT (I4,1X,F8.4)
99994 FORMAT (/' N is out of range.',/' N = ',I5)
END
Program Data
DE01PD EXAMPLE PROGRAM DATA 8 C N 0.4862 0.2288 0.1948 0.3671 0.5788 0.6417 -0.5861 0.3875 0.8254 0.2380 0.1815 0.4682 0.2904 0.5312 -0.3599 0.6116Program Results
DE01PD EXAMPLE PROGRAM RESULTS Convolution i A(i) 1 0.5844 2 0.5769 3 0.6106 4 1.0433 5 0.6331 6 0.4531 7 0.7027 8 0.9929