rfft1b rfft1f rfft1i

rfft1b() def rfft1b ( n  , r  , wsave  , inc  = 1  ) One-dimensional real fast Fourier backward transform Purpose rfft1b 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. Returns info (int) = 0: Successful exit = -1: The argument n had an illegal value (n < 1) = -2: The argument r is invalid = -3: The argument wsave is invalid = -4: The argument inc had an illegal value (inc < 1) 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 Numpy ndarray (1-dimensional, float, length inc*(n - 1) + 1) [in] The sequence to be transformed. [out] The Fourier backward transformed sequence of data. [in] wsave Numpy ndarray (1-dimensional, float, length 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. [in] inc (Optional) Integer increment between the locations, in array r, of two consecutive elements within the sequence. (inc >= 1) (default = 1) Reference FFTPACK 5.1 Example Program See example of rfft1f.