.Modelica.Math.FastFourierTransform.Internal.rawRealFFT

Information

Syntax

(info, amplitudes, phases) = rawRealFFT(u);

Description

Raw interface to a function of the Kiss_FFT package to compute the FFT of a real, sampled signal. The input argument of this function is a Real vector u. size(u,1) must be even. An efficient computation is performed, if size(u,1) = 2^a*3^b*5^c (a,b,c Integer ≥ 0). The function computes a real FFT (Fast Fourier Transform) of u and returns the result in form of the outputs amplitudes and phases. Argument info provides additional information:

info = 0: Successful FFT computation.
info = 1: size(u,1) is not even.
info = 2: size(work,1) is not correct (= a protected utility array).
info = 3: Another error.

Note, in the original publication about the efficient computation of FFT (Cooley and Tukey, 1965), the number of sample points must be 2^a. However, all newer FFT algorithms do not have this strong restriction and especially not the open source software KissFFT from Mark Borgerding used in this function.

References

Mark Borgerding (2010):

KissFFT, version 1.3.0. http://sourceforge.net/projects/kissfft/.
 

James W. Cooley, John W. Tukey (1965):

An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19: 297-301. doi:10.2307/2003354.
 

Martin R. Kuhn, Martin Otter, Tim Giese (2015):

Model Based Specifications in Aircraft Systems Design. Modelica 2015 Conference, Versailles, France, pp. 491-500, Sept.23-25, 2015. Download from: http://www.ep.liu.se/ecp/118/053/ecp15118491.pdf

Example

(info, A, phases) = realFFT({0,0.1,0.2,0.4,0.5, 0.6})

Interface

pure function rawRealFFT
  extends Modelica.Icons.Function;
  input Real u[:] "Signal for which FFT shall be computed (size(nu,1) MUST be EVEN and should be an integer multiple of 2,3,5, that is size(nu,1) = 2^a*3^b*5^c, with a,b,c Integer >= 0)";
  output Integer info "Information flag (0: FFT computed, 1: nu is not even, 2: nwork is wrong, 3: another error)";
  output Real amplitudes[div(size(u, 1), 2) + 1] "Amplitudes of FFT";
  output Real phases[div(size(u, 1), 2) + 1] "Phases of FFT";
end rawRealFFT;

Revisions