A parametric modeling approach to hubert transformation
Date of Original Version
A parametric approach to compute the Hilbert transform (HT) of a real signal is proposed. A scaled version of the real signal is raised to the exponent of Napier's base, and an all-pole signal model is fitted to approximate the resulting signal as though it were the envelope. An error criterion that flattens this envelope is then minimized over a set of complex Fourier coefficients. The resulting approximation is guaranteed to be a minimum-phase (MinP) signal. Since a MinP signal has the property that the logarithm of its envelope and its phase are related by HT, it follows that the resulting phase of MinP approximation yields the desired HT.
IEEE Signal Processing Letters
Rao, Ashwin, and Ramdas Kumaresan. "A parametric modeling approach to hubert transformation." IEEE Signal Processing Letters 5, 1 (1998): 15-17. doi:10.1109/97.654868.