Purpose
To apply an anti-aliasing window to a real signal.Specification
SUBROUTINE DK01MD( TYPE, N, A, INFO )
C .. Scalar Arguments ..
CHARACTER TYPE
INTEGER INFO, N
C .. Array Arguments ..
DOUBLE PRECISION A(*)
Arguments
Mode Parameters
TYPE CHARACTER*1
Indicates the type of window to be applied to the signal
as follows:
= 'M': Hamming window;
= 'N': Hann window;
= 'Q': Quadratic window.
Input/Output Parameters
N (input) INTEGER
The number of samples. N >= 1.
A (input/output) DOUBLE PRECISION array, dimension (N)
On entry, this array must contain the signal to be
processed.
On exit, this array contains the windowing function.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Method
If TYPE = 'M', then a Hamming window is applied to A(1),...,A(N),
which yields
_
A(i) = (0.54 + 0.46*cos(pi*(i-1)/(N-1)))*A(i), i = 1,2,...,N.
If TYPE = 'N', then a Hann window is applied to A(1),...,A(N),
which yields
_
A(i) = 0.5*(1 + cos(pi*(i-1)/(N-1)))*A(i), i = 1,2,...,N.
If TYPE = 'Q', then a quadratic window is applied to A(1),...,
A(N), which yields
_
A(i) = (1 - 2*((i-1)/(N-1))**2)*(1 - (i-1)/(N-1))*A(i),
i = 1,2,...,(N-1)/2+1;
_
A(i) = 2*(1 - ((i-1)/(N-1))**3)*A(i), i = (N-1)/2+2,...,N.
References
[1] Rabiner, L.R. and Rader, C.M.
Digital Signal Processing.
IEEE Press, 1972.
Numerical Aspects
The algorithm requires 0( N ) operations.Further Comments
NoneExample
Program Text
* DK01MD EXAMPLE PROGRAM TEXT
* Copyright (c) 2002-2010 NICONET e.V.
*
* .. Parameters ..
INTEGER NIN, NOUT
PARAMETER ( NIN = 5, NOUT = 6 )
INTEGER NMAX
PARAMETER ( NMAX = 20 )
* .. Local Scalars ..
CHARACTER*1 TYPE
INTEGER I, INFO, N
* .. Local Arrays ..
DOUBLE PRECISION A(NMAX)
* .. External Subroutines ..
EXTERNAL DK01MD
* .. Executable Statements ..
*
WRITE ( NOUT, FMT = 99999 )
* Skip the heading in the data file and read the data.
READ ( NIN, FMT = '()' )
READ ( NIN, FMT = * ) N, TYPE
IF ( N.LE.0 .OR. N.GT.NMAX ) THEN
WRITE ( NOUT, FMT = 99995 ) N
ELSE
READ ( NIN, FMT = * ) ( A(I), I = 1,N )
* Apply a Hamming window to the given signal.
CALL DK01MD( TYPE, N, A, INFO )
*
IF ( INFO.NE.0 ) THEN
WRITE ( NOUT, FMT = 99998 ) INFO
ELSE
WRITE ( NOUT, FMT = 99997 )
DO 20 I = 1, N
WRITE ( NOUT, FMT = 99996 ) I, A(I)
20 CONTINUE
END IF
END IF
STOP
*
99999 FORMAT (' DK01MD EXAMPLE PROGRAM RESULTS',/1X)
99998 FORMAT (' INFO on exit from DK01MD = ',I2)
99997 FORMAT (' Components of the windowing function are',//' k ',
$ ' A(k)',/)
99996 FORMAT (I4,3X,F8.4)
99995 FORMAT (/' N is out of range.',/' N = ',I5)
END
Program Data
DK01MD EXAMPLE PROGRAM DATA 8 M 0.3262 0.8723 -0.7972 0.6673 -0.1722 0.3237 0.5263 -0.3275Program Results
DK01MD EXAMPLE PROGRAM RESULTS Components of the windowing function are k A(k) 1 0.3262 2 0.8326 3 -0.6591 4 0.4286 5 -0.0754 6 0.0820 7 0.0661 8 -0.0262
Click here to get a compressed (gzip) tar file containing the source code of the routine, the example program, data, documentation, and related files.
Return to index