Performs the Fast Hilbert Transform over a double array.
Performs the Fast Hilbert Transform over a complex array.
The discrete Hilbert transform is a transformation operating on the time domain. It performs a 90 degree phase shift, shifting positive frequencies by +90 degrees and negative frequencies by -90 degrees. It is useful to create analytic representation of signals.
The Hilbert transform can be implemented efficiently by using the Fast Fourier Transform. After transforming a signal from the time-domain to the frequency domain, one can zero its negative frequency components and revert the signal back to obtain the phase shifting.
By applying the Hilbert transform to a signal twice, the negative of the original signal is recovered.