FFT complex numerical error

Summary

Finite numerical precision can result in very small imaginary parts, which turn the resulting signal complex.
Use real(...) on results, when expecting a real-valued result.

Limited numerical precision can lead to small imbalances between positive and negative frequencies.
This may lead to a very small but nonzero imaginary component. For example, if a unity signal results in an error of $10^{-15}$ , the relative power (magnitude squared) of the error is only $\frac{1}{3000000000000000000000000000000}$ !
However, some functionality in Matlab or Octave (example: plotting) will switch into complex mode if any imaginary part is encountered.
More than one novice user has been scratching his head over this issue, and the question remains popular on comp.dsp.
The solution is to use real(...) to remove the imaginary part.

© Markus Nentwig 2007-2008
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