Cost1b Cost1f Cost1i Costmb Costmf Costmi Sint1b Sint1f Sint1i Sintmb Sintmf Sintmi

Cost1f() Sub Cost1f ( N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional cosine transform Purpose This routine computes the one-dimensional Fourier transform of an even sequence within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. R(0) = (1/2)R(0)/(N-1) + ΣR(j)/(N-1) + (1/2)R(N-1)/(N-1) (Σ for j = 1 to N-2) R(k) = R(0)/(N-1) + Σ2R(j)cos(πjk/(N-1))/(N-1) + (-1)^k R(N-1)/(N-1) (Σ for j = 1 to N-2) (k = 1 to N-2) R(N-1) = (1/2)R(0)/(N-1) + ΣR(j)(-1)^k/(N-1) + (1/2)(-1)^(N-1) R(N-1)/(N-1) (Σ for j = 1 to N-2) This transform is normalized since a call to Cost1f followed by a call to Cost1b (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-1 is a product of small primes) [in,out] R() Array R(LR - 1) (LR >= 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 Cost1i before the first call to Cost1f or Cost1b for a given transform length N. [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 1) = -2: The argument R() is invalid. (Array R() 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 R(), of two consecutive elements within the sequence. (Inc >= 1) (default = 1) Reference FFTPACK Example Program Compute the cosine transform and backward transform of 5 random data sequence successively, and compare with the original data sequence. Sub Ex_Cost1() Const N = 5 Dim Wsave() As Double, R(N - 1) As Double, R0(N - 1) As Double Dim LWsave As Long, Info As Long, I As Long '-- Initialization LWsave = 2 * N + Log(N) / Log(2) + 4 ReDim Wsave(LWsave - 1) Call Cost1i(N, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To N - 1 R(I) = Rnd() R0(I) = R(I) Next '-- Forward transform Call Cost1f(N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cost1b(N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Print result For I = 0 To N - 1 Debug.Print R0(I), R(I), R(I) - R0(I) Next Exit Sub Err: Debug.Print "Error in Cost1i/Cost1f/Cost1b: Info =", Info End Sub Example Results 0.811601400375366 0.811601400375366 0 0.358389794826508 0.358389794826508 0 0.237738966941833 0.237738966941833 0 0.228048384189606 0.228048384189606 -5.55111512312578E-17 0.809549331665039 0.809549331665039 0