
The Fourier transform utility in FLUENT allows you to compute the Fourier transform of a signal, , a realvalued function, from a finite number of its sampled points.
The discrete Fourier transform of is defined by
Equation 28.107 and Equation 28.108 form a Fourier transform pair that allows us to determine one from the other.
Note that when we follow the convention of varying from 0 to in Equation 28.107 or Equation 28.108 instead of from to , the range of index corresponds to positive frequencies, and the range of index corresponds to negative frequencies. still corresponds to zero frequency.
For the actual calculation of the transforms, FLUENT adopts the socalled fast Fourier transform (FFT) algorithm which significantly reduces operation counts in comparison to the direct transform. Furthermore, unlike most FFT algorithms in which the number of data should be a power of 2, the FFT utility in FLUENT employs a primefactor algorithm [ 372]. The number of data points permissible in the primefactor FFT algorithm is any products of mutually prime factors from the set 2,3,4,5,7,8,9,11,13,16, with a maximum value of . Thus, the primefactor FFT preserves the original data better than the conventional FFT.
Just prior to computing the transform, FLUENT determines the largest permissible number of data points based on the prime factors, discarding the rest of the data.