DK01MD

Anti-aliasing window applied to a real signal

Purpose

  To apply an anti-aliasing window to a real signal.

      SUBROUTINE DK01MD( TYPE, N, A, INFO )
C     .. Scalar Arguments ..
      CHARACTER         TYPE
      INTEGER           INFO, N
C     .. Array Arguments ..
      DOUBLE PRECISION  A(*)

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.

  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.

  INFO    INTEGER
          = 0:  successful exit;
          < 0:  if INFO = -i, the i-th argument had an illegal
                value.

  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.

  [1] Rabiner, L.R. and Rader, C.M.
      Digital Signal Processing.
      IEEE Press, 1972.

  The algorithm requires 0( N ) operations.

  None

Program Text

*     DK01MD EXAMPLE PROGRAM TEXT
*     Copyright (c) 2002-2017 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

 DK01MD EXAMPLE PROGRAM DATA
   8     M
   0.3262
   0.8723
  -0.7972
   0.6673
  -0.1722
   0.3237
   0.5263
  -0.3275

 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

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