A parametric modeling approach to Hilbert transformation

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 the HT, it follows that the resulting phase of MinP approximation yields the desired HT.