## 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;

```
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
```   Rabiner, L.R. and Rader, C.M.
Digital Signal Processing.
IEEE Press, 1972.

```
Numerical Aspects
```  The algorithm requires 0( N ) operations.

```
```  None
```
Example

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
```
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
```