Rfft1b Rfft1f Rfft1i Rfftmb Rfftmf Rfftmi

Rfft1f() Sub Rfft1f ( N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional real Fourier transforms Purpose This routine computes the one-dimensional Fourier transform of a periodic 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/N)ΣR(j) (Σ for j = 0 to N-1) R(2k-1) = (2/N)ΣR(j)Cos(2πjk/N) (Σ for j = 0 to N-1) (k = 1 to NH) R(2k) = (2/N)ΣR(j)Sin(2πjk/N) (Σ for j = 0 to N-1) (k = 1 to NH) R(N-1) = (1/N)Σ(-1)^j R(j) (Σ for j = 0 to N-1) (only if N is even) (If N is even, NH = N/2-1. If N is odd, NH = (N-1)/2) This transform is normalized since a call to Rfft1f followed by a call to Rfft1b (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] 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 >= N + ln(N)/ln(2) + 4) Work data. Its contents must be initialized with a call to Rfft1i before the first call to Rfft1f or Rfft1b 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 Fourier transform and backward transform of 5 random data sequence successively, and compare with the original data sequence. Sub Ex_Rfft1() 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 = N + Log(N) / Log(2) + 4 ReDim Wsave(LWsave - 1) Call Rfft1i(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 Rfft1f(N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Rfft1b(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 Rfft1i/Rfft1f/Rfft1b: Info =", Info End Sub Example Results 0.705547511577606 0.705547511577606 1.11022302462516E-16 0.533424019813538 0.533424019813538 0 0.579518616199493 0.579518616199493 0 0.289562463760376 0.289562463760376 0 0.301948010921478 0.301948010921478 0