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http://dsp.stackexchange.com/questions/1406/real-discrete-fourier-transform

As far as I can tell there's a hypothetical efficiency argument. Am I wrong? I notice that a lot of computer algorithms are using the real version. For instance ffmpeg tends to use the real version as far as I can tell.

It seems to me that before computers, complex numbers were used to aid in hand computation. For instance it's easier to view sinusoidal functions as a power function of e than it is to calculate sines and cosines when you're doing it by hand.

Am I completely wrong about this analysis? In the case of Fourier transforms do I get missing data or have reduced accuracy when I use the real version instead of the complex version?

Thanks.