Cfft1b Cfft1f Cfft1i Cfftmb Cfftmf Cfftmi

Cfftmf() Sub Cfftmf ( Lot As  Long, Jump As  Long, N As  Long, C() As  Complex, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional complex Fourier transform (multiple sequences) Purpose This routine computes the one-dimensional Fourier transform of multiple periodic sequences within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. C(l*jump+k) = (1/N)ΣC(l*jump+j)exp(-2πijk/N) (Σ for j = 0 to N-1) (l = 0 to lot-1, k = 0 to N-1) (i is imaginary unit) This transform is normalized since a call to Cfftmf followed by a call to Cfftmb (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Parameters [in] Lot Number of sequences to be transformed. (Lot >= 1) [in] Jump Increment between the locations, in array C(), of the first elements of two consecutive sequences to be transformed. (Jump >= 1) [in] N Length of the sequence to be transformed. (N >= 1) (The transform is most efficient when N is a product of small primes) [in,out] C() Array C(LC - 1) (LC >= (Lot - 1)*Jump + IncC*(N - 1) + 1) [in] The sequences to be transformed. [out] The Fourier forward transformed sequences of data. [in] Wsave() Array Wsave(LWsave - 1) (LWsave >= 2*N + ln(N)/ln(2) + 4) Work data. Its contents must be initialized with a call to Cfftmi before the first call to Cfftmf or Cfftmb for a given transform length N. [out] Info = 0: Successful exit. = -1: The argument Lot had an illegal value. (Lot < 1, or, Lot, Jump, N and Inc are inconsistent) = -2: The argument Jump had an illegal value. (Jump < 1) = -3: The argument N had an illegal value. (N < 1) = -4: The argument C() had an illegal value. (Array C() is not big enough) = -5: The argument Wsave() had an illegal value. (Array Wsave() is not big enough) = -7: The argument Inc had an illegal value. (Inc < 1) [in] Inc (Optional) Integer increment between the locations, in array C(), of two consecutive elements within the sequence. (Inc >= 1) (default = 1) Reference FFTPACK Example Program Compute the Fourier transform and backward transform of 2 sequences of 5 random data successively, and compare with the original data sequences. Sub Ex_Cfftm() Const N = 5, Lot = 2, Jump = N Dim Wsave() As Double, C(Lot * N - 1) As Complex, C0(Lot * N - 1) As Complex Dim LWsave As Long, Info As Long, I As Long, J As Long, K As Long '-- Initialization LWsave = 2 * N + Log(N) / Log(2) + 4 ReDim Wsave(LWsave - 1) Call Cfftmi(N, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To Lot * N - 1 C(I) = Cmplx(Rnd(), Rnd()) C0(I) = Cmplx(Creal(C(I)), Cimag(C(I))) Next '-- Forward transform Call Cfftmf(Lot, Jump, N, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cfftmb(Lot, Jump, N, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Print result For J = 0 To Lot - 1 For I = 0 To N - 1 K = J * Jump + I Debug.Print "(" & CStr(Creal(C0(K))) & ", " & CStr(Cimag(C0(K))) & ")", "(" & CStr(Creal(C(K))) & ", " & CStr(Cimag(C(K))) & ")", Cabs(Csub(C(K), C0(K))) Next Debug.Print Next Exit Sub Err: Debug.Print "Error in Cfftmi/Cfftmf/Cfftmb: Info =", Info End Sub Example Results (0.661798179149628, 0.545043110847473) (0.661798179149628, 0.545043110847473) 1.57009245868378E-16 (0.403548061847687, 0.740813970565796) (0.403548061847687, 0.740813970565796) 1.24126707662364E-16 (0.678173959255219, 0.956120848655701) (0.678173959255219, 0.956120848655701) 3.14018491736755E-16 (3.96996140480042E-02, 0.474205017089844) (3.96996140480041E-02, 0.474205017089844) 7.85046229341888E-17 (0.802463710308075, 0.859862923622131) (0.802463710308075, 0.859862923622131) 2.48253415324727E-16 (0.748639404773712, 0.33688759803772) (0.748639404773712, 0.33688759803772) 0 (0.495910108089447, 0.185041308403015) (0.495910108089447, 0.185041308403015) 5.55111512312578E-17 (0.806551516056061, 0.312809467315674) (0.806551516056061, 0.312809467315674) 2.28878339926112E-16 (0.369169890880585, 0.412185788154602) (0.369169890880585, 0.412185788154602) 7.85046229341888E-17 (0.8343465924263, 0.351738691329956) (0.8343465924263, 0.351738691329956) 2.22044604925031E-16