Purpose
To compute the (scrambled) discrete Hartley transform of a real signal.Specification
SUBROUTINE DG01OD( SCR, WGHT, N, A, W, INFO )
C .. Scalar Arguments ..
CHARACTER SCR, WGHT
INTEGER INFO, N
C .. Array Arguments ..
DOUBLE PRECISION A(*), W(*)
Arguments
Mode Parameters
SCR CHARACTER*1
Indicates whether the signal is scrambled on input or
on output as follows:
= 'N': the signal is not scrambled at all;
= 'I': the input signal is bit-reversed;
= 'O': the output transform is bit-reversed.
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
Number of real samples. N must be a power of 2.
N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (N)
On entry with SCR = 'N' or SCR = 'O', this array must
contain the input signal.
On entry with SCR = 'I', this array must contain the
bit-reversed input signal.
On exit with SCR = 'N' or SCR = 'I', this array contains
the Hartley transform of the input signal.
On exit with SCR = 'O', this array contains the
bit-reversed Hartley transform.
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
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 uses a Hartley butterfly algorithm as described in [1].References
[1] Van Loan, Charles.
Computational frameworks for the fast Fourier transform.
SIAM, 1992.
Numerical Aspects
The algorithm is backward stable and requires O(N log(N)) floating point operations.Further Comments
NoneExample
Program Text
* DG01OD EXAMPLE PROGRAM TEXT
* Copyright (c) 2002-2010 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 SCR, WGHT
* .. Local Arrays ..
DOUBLE PRECISION A(NMAX), W(NMAX)
* .. External Subroutines ..
EXTERNAL DG01OD
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N, SCR, WGHT
IF ( N.LT.0 .OR. N.GT.NMAX ) THEN
WRITE ( NOUT, FMT = 99995 ) N
ELSE
READ ( NIN, FMT = * ) ( A(I), I = 1,N )
* Compute the Hartley transform.
CALL DG01OD( SCR, WGHT, N, A, W, INFO )
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
DO 10 I = 1, N
WRITE ( NOUT, FMT = 99996 ) I, A(I)
10 CONTINUE
END IF
END IF
STOP
*
99999 FORMAT (' DG01OD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from DG01OD = ',I2)
99997 FORMAT (' Hartley transform ',//' i A(i)',/)
99996 FORMAT (I4,1X,F8.4)
99995 FORMAT (/' N is out of range.',/' N = ',I5)
END
Program Data
DG01OD EXAMPLE 16 N N 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0Program Results
DG01OD EXAMPLE PROGRAM RESULTS Hartley transform i A(i) 1 136.0000 2 -48.2187 3 -27.3137 4 -19.9728 5 -16.0000 6 -13.3454 7 -11.3137 8 -9.5913 9 -8.0000 10 -6.4087 11 -4.6863 12 -2.6546 13 0.0000 14 3.9728 15 11.3137 16 32.2187
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