Cfft2b Cfft2f Cfft2i Rfft2b Rfft2c Rfft2f Rfft2i

Rfft2b() Sub Rfft2b ( L As  Long, M As  Long, R() As  Double, Wsave() As  Double, Info As  Long  ) Two-dimensional real Fourier backward transform Purpose This routine computes the two-dimensional Fourier transform of a periodic sequence within a real array. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space. R(j,k) = ΣΣc(l1,m1)exp(2πi(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 Rfft2b followed by a call to Rfft2f (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Parameters [in] L Number of elements to be transformed in the first dimension of the two-dimensional array R(). (L >= 1) (The transform is most efficient when L is a product of small primes) [in] M Number of elements to be transformed in the second dimension of the two-dimensional array R(). (M >= 1) (The transform is most efficient when M is a product of small primes) [in,out] R() Array R(LR1 - 1, LR2 - 1) (LR1 >= L, LR2 >= M) [in] The two dimensional complex sequence data to be transformed (packed conjugate symmetric data as decsribed in the documentation of Rfft2f). [out] The Fourier backward transformed two dimensional real sequence data. [in] Wsave() Array Wsave(LWsave - 1) (LWsave >= L + 3*M + ln(L)/ln(2) + 2*ln(M)/ln(2) + 12) 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 L and 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 R() is invalid. (Array R() is not big enough) = -4: The argument Wsave() is invalid. (Array Wsave() is not big enough) Reference FFTPACK Example Program See example of Rfft2f.