Cfft1b Cfft1f Cfft1i Cfftmb Cfftmf Cfftmi

Cfft1f() Sub Cfft1f ( N As  Long, C() As  Complex, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional complex Fourier transform Purpose This routine computes the one-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(k) = (1/N)ΣC(j)exp(-2πijk/N) (Σ for j = 0 to N-1) (k = 0 to N-1) (i is imaginary unit) This transform is normalized since a call to Cfft1f followed by a call to Cfft1b (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Parameters [in] N The 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 >= Inc*(N - 1) + 1) [in] The sequence to be transformed. [out] The Fourier forward transformed sequence 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 Cfft1i before the first call to Cfft1f or Cfft1b for a given transform length N. [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 1) = -2: The argument C() is invalid. (Array C() is not big enough) = -3: The argument Wsave() is invalid. (Array Wsave() is not big enough) = -5: 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 5 random data sequence successively, and compare with the original data sequence. Sub Ex_Cfft1() Const N = 5 Dim Wsave() As Double, C(N - 1) As Complex, C0(N - 1) As Complex Dim LWsave As Long, Info As Long, I As Long '-- Initialization LWsave = 2 * N + Log(N) / Log(2) + 4 ReDim Wsave(LWsave - 1) Call Cfft1i(N, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To N - 1 C(I) = Cmplx(Rnd(), Rnd()) C0(I) = Cmplx(Creal(C(I)), Cimag(C(I))) Next '-- Forward transform Call Cfft1f(N, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cfft1b(N, C(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Print result For I = 0 To N - 1 Debug.Print "(" & CStr(Creal(C0(I))) & ", " & CStr(Cimag(C0(I))) & ")", "(" & CStr(Creal(C(I))) & ", " & CStr(Cimag(C(I))) & ")", Cabs(Csub(C(I), C0(I))) Next Exit Sub Err: Debug.Print "Error in Cfft1i/Cfft1f/Cfft1b: Info =", Info End Sub Example Results (0.961953163146973, 0.871445834636688) (0.961953163146973, 0.871445834636688) 0 (5.62368631362915E-02, 0.949556648731232) (5.62368631362915E-02, 0.949556648731232) 0 (0.364018678665161, 0.524868428707123) (0.364018678665161, 0.524868428707123) 5.55111512312578E-17 (0.767111659049988, 5.35045266151428E-02) (0.767111659049988, 5.35045266151427E-02) 1.11022302462516E-16 (0.592458248138428, 0.468700110912323) (0.592458248138428, 0.468700110912323) 5.55111512312578E-17