Cfft2b Cfft2f Cfft2i Rfft2b Rfft2c Rfft2f Rfft2i

Cfft2f() Sub Cfft2f ( L As  Long, M As  Long, C() As  Complex, Wsave() As  Double, Info As  Long  ) Two-dimensional complex Fourier transform Purpose This routine computes the two-dimensional Fourier transform of a periodic sequence within a complex array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. C(j,k) = (1/lm)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 Cfft2f followed by a call to Cfft2b (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 C(). (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 C(). (M >= 1) (The transform is most efficient when M is a product of small primes) [in,out] C() Array C(LC1 - 1, LC2 - 1) (LC1 >= L, LC2 >= M) [in] The two dimensional sequence dat to be transformed. [out] Fourier forward transformed two dimensional sequence data. [in] Wsave() Array Wsave(LWsave - 1) (LWsave >= 2*(L+M) + ln(L)/ln(2) + Ln(M)/Ln(2) + 8) Work data. Its contents must be initialized with a call to Cfft2i before the first call to Cfft2f or Cfft2b 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 C() is invalid. (Array C() is not big enough) = -4: The argument Wsave() is invalid. (Array Wsave() is not big enough) Reference FFTPACK Example Program Compute the two-dimensional Fourier transform and backward transform of 4 rows x 4 columns random complex data sequence successively, and compare with the original data sequence. Sub Ex_Cfft2() Const L = 4, M = 4 Dim Wsave() As Double, C(L - 1, M - 1) As Complex, C0(L - 1, M - 1) As Complex Dim LWsave As Long, Info As Long, I As Long, J As Long '-- Initialization LWsave = 2 * (L + M) + Log(L) / Log(2) + Log(M) / Log(2) + 8 ReDim Wsave(LWsave - 1) Call Cfft2i(L, M, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To L - 1 For J = 0 To M - 1 C(I, J) = Cmplx(Rnd(), Rnd()) C0(I, J) = Cmplx(Creal(C(I, J)), Cimag(C(I, J))) Next Next '-- Forward transform Call Cfft2f(L, M, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cfft2b(L, M, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Print result For J = 0 To M - 1 For I = 0 To L - 1 Debug.Print "(" & CStr(Creal(C0(I, J))) & ", " & CStr(Cimag(C0(I, J))) & ")", "(" & CStr(Creal(C(I, J))) & ", " & CStr(Cimag(C(I, J))) & ")", Cabs(Csub(C(I, J), C0(I, J))) Next Debug.Print Next Exit Sub Err: Debug.Print "Error in Cfft2i/Cfft2f/Cfft2b: Info =", Info End Sub Example Results (0.72104674577713, 2.41577625274658E-02) (0.72104674577713, 2.41577625274658E-02) 0 (0.603598415851593, 0.117225408554077) (0.603598415851593, 0.117225408554077) 0 (0.341512024402618, 0.784832239151001) (0.341512024402618, 0.784832239151001) 0 (0.734103977680206, 0.129029035568237) (0.734103977680206, 0.129029035568237) 0 (0.620623052120209, 0.25133216381073) (0.620623052120209, 0.25133216381073) 0 (0.619252145290375, 0.921948790550232) (0.619252145290375, 0.921948790550232) 0 (0.472388684749603, 0.294668078422546) (0.472388684749603, 0.294668078422546) 0 (0.373880326747894, 0.287947058677673) (0.373880326747894, 0.287947058677673) 0 (0.286389887332916, 0.837161540985107) (0.286389887332916, 0.837161540985107) 0 (0.77502828836441, 0.369781494140625) (0.77502828836441, 0.369781494140625) 0 (0.360483705997467, 2.57539749145508E-03) (0.360483705997467, 2.57539749145508E-03) 0 (0.787385046482086, 1.65653228759766E-03) (0.787385046482086, 1.65653228759766E-03) 0 (0.904512107372284, 0.480963826179504) (0.904512107372284, 0.480963826179504) 0 (0.811046779155731, 0.748176217079163) (0.811046779155731, 0.748176217079163) 0 (0.245184600353241, 0.948204159736633) (0.245184600353241, 0.948204159736633) 0 (0.908585727214813, 0.476067185401917) (0.908585727214813, 0.476067185401917) 0