Two-Dimensional Fourier Transform

Calling Sequence

CALL RFFT2B	(PLACE, FULL, M, N, RX, LDX, RY, LDY, RWSAVE, LWSAVE)
CALL DFFT2B	(PLACE, FULL, M, N, DX, LDX, DY, LDY, DWSAVE, LWSAVE)
CALL CFFT2B	(M, N, CX, LDX, CWSAVE, LWSAVE)
CALL ZFFT2B	(M, N, ZX, LDX, ZWSAVE, LWSAVE)
void rfft2b	(char place, char full, int m, int n, float *rx, int ldx, float *ry, int ldy, float *wsave, int lwsave)
void dfft2b	(char place, char full, int m, int n, double *dx, int ldx, double *dy, int idy, double *wsave, int lwsave)
void cfft2b	(int m, int n, complex *cx, int ldx, complex *wsave, int lwsave)
void zfft2b	(int m, int n, doublecomplex *zx, int ldx, doublecomplex *wsave, int lwsave)

Arguments

PLACE	Indicates whether the transform should be performed in place or out-of-place. The legal values for PLACE are listed below. Any values not listed below are illegal. `I' or `i' In-place. Input is supplied in xX and the transformed input is returned in xX. xY is not referenced. `O' or `o' Out-of-place. Input is supplied in xX and the transformed input is returned in xY.
FULL	Indicates whether the transform is to take advantage of conjugate symmetry in the complex result. If it should use symmetry then it will write only the first half of the result, otherwise it will write the entire result. Writing the entire result requires twice as much storage. `F' or `f' Return the full result and do not take advantage of symmetry. `N' or `n' Return the first half of the result.
M	Number of rows to be transformed. These subroutines are most efficient when M is a product of small primes. M 0.
N	Length of the sequence(s) to be transformed. These subroutines are most efficient when N is a product of small primes. N 0.
xX	On entry, a two-dimensional array xX(M,N) that contains the sequences to be transformed.
LDX	Leading dimension of the array containing the data to be transformed. LDX M.
xY	Undefined on entry. On exit, the transformed sequence in the transform is performed out of place, otherwise undefined.
LDY	Leading dimension of the output array. LDY M.
xWSAVE	On entry, an array with dimension of at least (M + N + MAX(M,N) + 45). The array must have been initialized by xFFT2I.
LWSAVE	On entry, the length of WSAVE. Unchanged on output.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LWSAVE, M, N

PARAMETER (M = 2)

PARAMETER (N = 4)

PARAMETER (LWSAVE = 4 * (M + N + N) + 40)

C

INTEGER I, J

REAL PI, WSAVE(LWSAVE)

REAL X, Y

COMPLEX C(M,N)

C

EXTERNAL CFFT2B, CFFT2F, CFFT2I

INTRINSIC ACOS, CMPLX, COS, SIN

C

C Initialize the array C to a complex sequence.

C

PI = ACOS (-1.0)

DO 110, J = 1, N

DO 100, I = 1, M

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

Y = COS ((J - 1.0) * 2.0 * PI / M)

C(I,J) = CMPLX (X, Y)

100 CONTINUE

110 CONTINUE

C

PRINT 1000

DO 200, I = 1, M

PRINT 1010, (C(I,J), J = 1, N)

200 CONTINUE

CALL CFFT2I (M, N, WSAVE)

CALL CFFT2F (M, N, C, M, WSAVE, LWSAVE)

PRINT 1020

DO 300, I = 1, M

PRINT 1010, (C(I,J), J = 1, N)

300 CONTINUE

CALL CFFT2B (M, N, C, M, WSAVE, LWSAVE)

PRINT 1030

DO 400, I = 1, M

PRINT 1010, (C(I,J), J = 1, N)

400 CONTINUE

C

1000 FORMAT (1X, `Original Sequences:')

1010 FORMAT (1X, 100(F4.1' +',F4.1,'i `))

1020 FORMAT (1X, `Transformed Sequences:')

1030 FORMAT (1X, `Recovered Sequences:')

C

END

Sample Output

0.0 + 1.0i 0.0 +-1.0i 0.0 + 1.0i 0.0 +-1.0i

1.0 + 1.0i 1.0 +-1.0i 1.0 + 1.0i 1.0 +-1.0i

Transformed Sequences:

4.0 + 0.0i 0.0 + 0.0i 0.0 + 8.0i 0.0 + 0.0i

-4.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i 0.0 + 0.0i

Recovered Sequences:

0.0 + 8.0i 0.0 +-8.0i 0.0 + 8.0i 0.0 +-8.0i

8.0 + 8.0i 8.0 +-8.0i 8.0 + 8.0i 8.0 +-8.0i