◆ rfft1b()

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.

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]	inc	Integer increment between the locations, in array r[], of two consecutive elements within the sequence. (inc >= 1)
[in,out]	r[]	Array r[lr] [in] The sequence to be transformed. [out] The Fourier backward transformed sequence of data.
[in]	lr	The length of the array r[]. (lr >= inc*(n - 1) + 1)
[in]	wsave[]	Array wsave[lwsave] 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]	lwsave	The length of the array wsave[]. (lwsave >= n + ln(n)/ln(2) + 4)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= n)
[out]	info	= 0: Successful exit = -1: The argument n had an illegal value (n < 1) = -2: The argument inc had an illegal value (inc < 1) = -4: The argument lr had an illegal value (lr not big enough) = -6: The argument lwsave had an illegal value (lwsave not big enough) = -8: The argument lwork had an illegal value (lwork not big enough)