◆ rfft1f()

One-dimensional real Fourier transform

Purpose: rfft1f computes the one-dimensional Fourier transform of a periodic sequence within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space.
r[0] = (1/n)Σr[j] (Σ for j = 0 to n-1)

r[2k-1] = (2/n)Σr[j]cos(2πjk/n) (Σ for j = 0 to n-1) (k = 1 to nh)

r[2k] = (2/n)Σr[j]sin(2πjk/n) (Σ for j = 0 to n-1) (k = 1 to nh)

r[n-1] = (1/n)Σ(-1)^j r[j] (Σ for j = 0 to n-1) (only if n is even)

(If n is even, nh = n/2-1. If n is odd, nh = (n-1)/2)

This transform is normalized since a call to rfft1f followed by a call to rfft1b (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 forward 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)