Hilbert Transform and Applications

When x(t) is narrow-banded, |z(t)| can be regarded as a slow-varying envelope of x(t) while the phase derivative ∂t[tan −1(y/x)] is an instantaneous frequency. Thus, Hilbert transform can be interpreted as a way to represent a narrow-band signal in terms of amplitude and frequency modulation. The transform is therefore useful for diverse purposes such as latency analysis in neuro-physiological signals (Recio-Spinoso et al., 2011; van Drongelen, 2007), design of bizarre stimuli for psychoacoustic experiments (Smith et al., 2002), speech data compression for communication (Potamianos & Maragos, 1994), regularization of convergence problems in multi-channel acoustic echo cancellation (Liu & Smith, 2002), and signal processing for auditory prostheses (Nie et al., 2006).