cfft2b cfft2f cfft2i rfft2b rfft2c rfft2f rfft2i

rfft2f() void rfft2f ( int  l, int  m, int  ldr, double  r[], double  wsave[], int  lwsave, double  work[], int  lwork, int *  info  ) Two-dimensional real Fourier transform Purpose rfft2f computes the two-dimensional Fourier transform of a periodic sequence within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. The full complex transform is given by: c[k][j] = (1/lm)ΣΣr[m1][l1]exp(-2π*i(j*l1/l+k*m1/m)) (1st Σ for l1 = 0 to l-1, 2nd Σ for m1 = 0 to m-1) (j = 0 to l-1, k = 0 to m-1) (i is imaginary unit) This transform is normalized since a call to rfft2f followed by a call to rfft2b (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Parameters [in] l The number of elements to be transformed in the first dimension of the two-dimensional data array. (l >= 1) The transform is most efficient when l is a product of small primes. [in] m The number of elements to be transformed in the second dimension of the two-dimensional data array. (m >= 1) The transform is most efficient when m is a product of small primes. [in] ldr Leading dimension of two dimensional array r[][]. (ldr >= l) [in,out] r[] Array r[lr][ldr] (lr >= m) [in] The two dimensional real sequence data to be transformed. [out] The Fourier forward transformed two dimensional complex sequence data c(i,j) (i = 0 to l-1, j = 0 to m-1).   The complex transform of the real sequence data has conjugate symmetry. That is, c(i,j) = conj(c(l-i,m-j)), so only half the transform is computed and packed back into the original array r[] as shown in the examples below. [in] wsave[] Array wsave[lwsave] Work data. Its contents must be initialized with a call to rfft2i before the first call to rfft2f or rfft2b for a given transform length n. [in] lwsave The length of the array wsave[]. (lwsave >= l+3m+ln(l)/ln(2)+2ln(m)/ln(2)+12) [out] work[] Array work[lwork] Work array. [in] lwork The length of the array work[]. (lwork >= (l + 1)*m) [out] info = 0: Successful exit = -1: The argument l had an illegal value (l < 1) = -2: The argument m had an illegal value (m < 1) = -3: The argument ldr had an illegal value (ldr < l) = -6: The argument lwsave had an illegal value (lwsave not big enough) = -8: The argument lwork had an illegal value (lwork not big enough) Further Details Let a(i,j) = re(c(i,j)) and b(i,j) = im(c(i,j)), then the packed data of the forward transform are stored in r[][] as following examples: l = m = 4 a(0,0)* a(0,1) b(0,1) a(0,2)* r[][] = a(1,0) a(1,1) a(1,2) a(1,3) b(1,0) b(1,1) b(1,2) b(1,3) a(2,0)* a(2,1) b(2,1) a(2,2)* l = m = 5 a(0,0)* a(0,1) b(0,1) a(0,2) b(0,2) a(1,0) a(1,1) a(1,2) a(1,3) a(1,4) r[][] = b(1,0) b(1,1) b(1,2) b(1,3) b(1,4) a(2,0) a(2,1) a(2,2) a(2,3) a(2,4) b(2,0) b(2,1) b(2,2) b(2,3) b(2,4) *: Imaginary part = 0 The remaining c(i,j) for i = (l+1)/2 to l-1 and j = 0 to m-1 can be obtained via the conjugate symmetry. For even l, c(l/2,j) = conj(c(l/2,m-j). Reference FFTPACK 5.1