Cosine Even-Wave Transform

For i=1,...,n

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Note - The xCOST transforms are unnormalized inverses of themselves, so a call of xCOST followed by another call of xCOST will multiply the input sequence by 2 × (N-1). The VxCOST transforms are normalized, so a call of VxCOST followed by a call of VxCOST will return the original sequence.

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Calling Sequence

CALL COST	(N, RX, RWSAVE)
CALL DCOST	(N, DX, DWSAVE)
CALL VCOST	(M,N, RX, RXT, MDIMX, RWSAVE)
CALL VDCOST	(M,N, DX, DXT, MDIMX, DWSAVE)
void cost	(int n, float *rx, float *rwsave)
void dcost	(int n, double *dx, double *dwsave)
void vcost	(int m, int n, float *rx, int mdimx, float *rwsave)
void vdcost	(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-1 is a product of small primes. N 2.
xX	On entry, an array of length N containing the sequence to be transformed. For VxCOST, a real two-dimensional array with dimensions of (MDIMX × N) whose rows contain the sequences to be transformed. On exit, the cosine transform of the input.
xXT	(For vector operations only.) A real two-dimensional work array with dimensions of (MDIMX × (N-1)).
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), initialized by xCOSTI or VxCOSTI.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER N

PARAMETER (N = 9)

C

INTEGER I

REAL PI, X(N), WSAVE(3 * N + 15)

C

EXTERNAL COST, COSTI

INTRINSIC ACOS, COS

C

C Initialize the array X to an even sequence, that is, it

C can be expanded in terms of a trigonometric series that

C contains only cosine terms.

C

PI = ACOS (-1.0)

DO 100, I=1, N

X(I) = COS ((I - 1.0) * 2.0 * PI / (N - 1.0))

100 CONTINUE

C

CALL COSTI (N, WSAVE)

PRINT 1000

PRINT 1010, (X(I), I = 1, N)

CALL COST (N, X, WSAVE)

PRINT 1020

PRINT 1010, (X(I), I = 1, N)

CALL COST (N, X, WSAVE)

PRINT 1030

PRINT 1010, (X(I), I = 1, N)

C

1000 FORMAT (1X, 'Original Sequence: ')

1010 FORMAT (1X, 100(F5.1, 1X))

1020 FORMAT (1X, 'Transformed Sequence: ')

1030 FORMAT (1X, 'Recovered Sequence: ')

END

Sample Output

Original Sequence:
1.0 0.7 0.0 -0.7 -1.0 -0.7 0.0 0.7 1.0
Transformed Sequence:
0.0 0.0 8.0 0.0 0.0 0.0 0.0 0.0 0.0
Recovered Sequence:
16.0 11.3 0.0 -11.3 -16.0 -11.3 0.0 11.3 16.0