Cosq1f Cosq1i Cosqmb Cosqmf Cosqmi Sinq1b Sinq1f Sinq1i Sinqmb Sinqmf Sinqmi

Sinq1b() Sub Sinq1b ( N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional quarter sine backward transform Purpose This routine computes the one-dimensional Fourier transform of a sequence which is a sine series with odd wave numbers. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space. R(j) = ΣR(k)sin(π(j+1)(2k+1)/(2n)) (Σ for k = 0 to N-1) (j = 0 to N-1) This transform is normalized since a call to Sinq1b followed by a call to Sinq1f (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 >= 2*N + ln(N)/ln(2) + 4) Work data. Its contents must be initialized with a call to Sinq1i before the first call to Sinq1f or Sinq1b 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 Sinq1f.