Cosq1f Cosq1i Cosqmb Cosqmf Cosqmi Sinq1b Sinq1f Sinq1i Sinqmb Sinqmf Sinqmi

Cosq1f() Sub Cosq1f ( N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional quarter cosine transform Purpose This routine computes the one-dimensional Fourier transform of a sequence which is a cosine series with odd wave numbers. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. R(k) = R(0)/N + (2/N)ΣR(j)cos(πj(2k+1)/(2n)) (Σ for j = 1 to N-1) (k = 0 to N-1) This transform is normalized since a call to Cosq1f followed by a call to Cosq1b (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 >= 2*N + ln(N)/ln(2) + 4) Work data. Its contents must be initialized with a call to Cosq1i before the first call to Cosq1f or Cosq1b 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_Cosq1() 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 Cosq1i(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 Cosq1f(N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cosq1b(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 Cosq1i/Cosq1f/Cosq1b: Info =", Info End Sub Example Results 0.90998101234436 0.90998101234436 0 0.436786115169525 0.436786115169525 0 0.381944537162781 0.381944537162781 1.11022302462516E-16 0.157248079776764 0.157248079776764 2.77555756156289E-17 0.436501026153564 0.436501026153564 0