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Sine Quarter-Wave Transform

The subroutines described in this section compute the Fourier coefficients in a sine series representation with only odd wave numbers. The transform is defined as:

For i=1,...,n


Note - The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 × N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.

Calling Sequence

CALL SINQF 
(N, RX, RWSAVE)
CALL DSINQF 
(N, DX, DWSAVE)
CALL VSINQF 
(M, N, RX, RXT, MDIMX, RWSAVE)
CALL VDSINQF 
(M, N, DX, DXT, MDIMX, DWSAVE)
 



void sinqf 
(int n, float *rx, float *rwsave)
void dsinqf 
(int n, double *dx, double *dwsave)
void vsinqf 
(int m, int n, float *rx, int mdimx, float *rwsave)
void vdsinqf 
(int m, int n, double *dx, int mdimx, double *dwsave)

Arguments

M

(For vector operations only.)
The number of sequences to be transformed. M 0.

N

Length of the sequence to be transformed. These subroutines are most efficient when N is a product of small primes. N 0.

xX

On entry, an array of length N containing the sequence to be transformed. For VxSINQF, a real two-dimensional array with dimensions of (MDIMX × N) whose rows contain the sequences to be transformed. On exit, the quarter-wave sine transform of the input.

xXT

(For vector operations only.)
A real two-dimensional work array with dimensions of (MDIMX × N).

MDIMX

(For vector operations only.)
Leading dimension of the arrays xX and xXT as specified in a dimension or type statement. MDIMX M.

xWSAVE

On entry, an array with dimension of at least (3 × N + 15) for scalar subroutines or (2 × N + 15) for vector subroutines, initialized by xSINQI or VxSINQI.

Sample Program

 
      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           M, N
      PARAMETER        (M = 4) 
      PARAMETER        (N = 6) 
C
      INTEGER           I, J
      REAL              PI, WSAVE(N + 15), X(M, N+1), XT(M, N + 1)
C
      EXTERNAL          VSINQB, VSINQF, VSINQI
      INTRINSIC         ACOS, SIN
C
C     Initialize the array to m real odd quarter-wave sequence, 
C     that is, they can be expanded in terms of a cosine series
C     with only odd wave numbers.  
C
      PI = ACOS (-1.0)
      DO 110, J=1, M
        DO 100, I=1, N
          X(J,I) = 40.0 * J * SIN (I * PI / (2.0 * N))
  100   CONTINUE
  110 CONTINUE
C
      CALL VSINQI (N, WSAVE) 
      PRINT 1000 
      DO 120, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
  120 CONTINUE
      CALL VSINQF (M, N, X, XT, M, WSAVE)
      PRINT 1020 
      DO 130, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
  130 CONTINUE
      CALL VSINQB (M, N, X, XT, M, WSAVE)
      PRINT 1030 
      DO 140, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
  140 CONTINUE
C
 1000 FORMAT (1X, 'Original Sequence: ') 
 1010 FORMAT (1X, '  Sequence', I2, ':  ', 100(F5.1, 1X))
 1020 FORMAT (1X, 'Transformed Sequence: ')
 1030 FORMAT (1X, 'Recovered Sequence: ')
C
      END
 

Sample Output

 
 Original Sequence: 
   Sequence 1:   10.4  20.0  28.3  34.6  38.6  40.0
   Sequence 2:   20.7  40.0  56.6  69.3  77.3  80.0
   Sequence 3:   31.1  60.0  84.9 103.9 115.9 120.0
   Sequence 4:   41.4  80.0 113.1 138.6 154.5 160.0
 Transformed Sequence: 
   Sequence 1:   49.0   0.0   0.0   0.0   0.0   0.0
   Sequence 2:   98.0   0.0   0.0   0.0   0.0   0.0
   Sequence 3:  147.0   0.0   0.0   0.0   0.0   0.0
   Sequence 4:  196.0   0.0   0.0   0.0   0.0   0.0
 Recovered Sequence: 
   Sequence 1:   10.4  20.0  28.3  34.6  38.6  40.0
   Sequence 2:   20.7  40.0  56.6  69.3  77.3  80.0
   Sequence 3:   31.1  60.0  84.9 103.9 115.9 120.0
   Sequence 4:   41.4  80.0 113.1 138.6 154.5 160.0






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