Cosq1f Cosq1i Cosqmb Cosqmf Cosqmi Sinq1b Sinq1f Sinq1i Sinqmb Sinqmf Sinqmi

Cosqmf() Sub Cosqmf ( Lot As  Long, Jump As  Long, N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional quarter cosine transform (multiple sequences) Purpose This routine computes the one-dimensional Fourier transform of multiple sequences within a real array, where each of a sequence 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(l*jump+k) = R(l*jump)/N + (2/N)ΣR(l*jump+j)cos(πj(2k+1)/(2n)) (Σ for j = 1 to N-1) (l = 0 to lot-1, k = 0 to N-1) This transform is normalized since a call to Cosqmf followed by a call to Cosqmb (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 R(), 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] R() Array R(LR - 1) (LR >= (Lot - 1)*Jump + Inc*(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 Cosqmi before the first call to Cosqmf or Cosqmb 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 R() had an illegal value. (Array R() 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 R(), of two consecutive elements within the sequence. (Inc >= 1) (default = 1) Reference FFTPACK Example Program Compute the cosine transform and backward transform of 2 sequences of 5 random data successively, and compare with the original data sequences. Sub Ex_Cosqm() Const N = 5, Lot = 2, Jump = N Dim Wsave() As Double, R(Lot * N - 1) As Double, R0(Lot * N - 1) As Double 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 Cosqmi(N, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To Lot * N - 1 R(I) = Rnd() R0(I) = R(I) Next '-- Forward transform Call Cosqmf(Lot, Jump, N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Cosqmb(Lot, Jump, N, R(), 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 R0(K), R(K), R(K) - R0(K) Next Debug.Print Next Exit Sub Err: Debug.Print "Error in Cosqmi/Cosqmf/Cosqmb: Info =", Info End Sub Example Results 0.470751464366913 0.470751464366913 5.55111512312578E-17 0.689472317695618 0.689472317695618 0 0.256393253803253 0.256393253803253 1.11022302462516E-16 0.323879957199097 0.323879957199097 1.11022302462516E-16 0.504171311855316 0.504171311855316 0 0.752542853355408 0.752542853355408 2.22044604925031E-16 0.827191412448883 0.827191412448883 0 0.581456184387207 0.581456184387207 0 7.15305209159851E-02 7.15305209159852E-02 5.55111512312578E-17 0.280201554298401 0.280201554298401 -5.55111512312578E-17