Rfft1b Rfft1f Rfft1i Rfftmb Rfftmf Rfftmi

Rfft1b() Sub Rfft1b ( N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional real fast Fourier backward transform Purpose This routine computes the one-dimensional Fourier transform of a periodic sequence 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(K) = R(0) + (-1)^k R(N-1) + ΣR(2j-1)Cos(2πjk/N) + ΣR(2j)Sin(2πjk/N) (Σ for j = 1 to N/2-1) (k = 0 to N-1) When N is odd: R(K) = R(0) + ΣR(2j-1)Cos(2πjk/N) + ΣR(2j)Sin(2πjk/N) (Σ for j = 1 to (N-1)/2) (k = 0 to N-1) This transform is normalized since a call to Rfft1b followed by a call to Rfft1f (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 backward 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 See example of Rfft1f.