## DK01MD

### Anti-aliasing window applied to a real signal

[Specification] [Arguments] [Method] [References] [Comments] [Example]

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

      None

Example

Program Text

    *     DK01MD EXAMPLE PROGRAM TEXT
    *
    *     .. 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
      -0.3275

Program 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

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