Rfft1b Rfft1f Rfft1i Rfftmb Rfftmf Rfftmi

Rfftmb() Sub Rfftmb ( 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 real Fourier backward transform (multiple sequences) Purpose This routine computes the one-dimensional Fourier transform of periodic sequences within a real array. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space. When N is even: R(l*Jump+k) = R(l*Jump) + (-1)^k R(l*Jump+N-1) + ΣR(l*Jump+2j-1)cos(2πjk/N) + ΣR(l*Jump+2j)sin(2πjk/N) (Σ for j = 1 to N/2-1) (l = 0 to Lot-1, k = 0 to N-1) When N is odd: R(l*Jump+k) = R(l*Jump) + ΣR(l*Jump+2j-1)cos(2πjk/N) + ΣR(l*Jump+2j)sin(2πjk/N) (Σ for j = 1 to (N-1)/2) (l = 0 to Lot-1, k = 0 to N-1) This transform is normalized since a call to Rfftmb followed by a call to Rfftmf (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 backward transformed sequences 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 Rfftmi before the first call to Rfftmf or Rfftmb 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 See example of Rfftmf.