# Hermitian FFT vs discrete Fourier transform. Python's $\tt hfft$ vs $\tt fft$

What is the difference between the Hermitian FFT and DFT? Particularly in Python, there are two functions fft and hfft.

numpy.fft.hfft(signal) vs numpy.fft.fft(signal)


What I simply could find out is: The Hermitian has to do something with symmetry and needs 50 times longer to calculate, while producing a 'slightly' different result than the 'discrete' FFT. (tested on an audio file of machinery sounds and length of 1.5 sec).

• hfft is basically the same as irfft (just with different sign convention). – Are you sure these are ever faster or more accurate? Actually I'd suspect they're all implemented with the same fft primitive and just automatically take care of adding/removing the symmetry-redundant parts of the signal or imaginary parts of the spectrum. – leftaroundabout Mar 28 '17 at 14:40
• i never heard it called "hfft()" – robert bristow-johnson Mar 29 '17 at 7:03