Fast spectral estimation of speech signal in analytic form

The analytic form of speech signals has been generated by combining the real-valued speech with its imaginary-valued discrete-Hilbert-transformed counter-part. Instead of using an 8th order real-valued linear prediction to analyze its spectral components, a 4th order complex-valued linear prediction is used. Furthermore, a fast and closed-form rooting procedure is adopted to extract the roots (i.e., bandwidth and frequency information of the speech formants) of the obtained 4th order polynomial of the corresponding inverse filter. The numerical complexity and convergence problems are thus avoided and the computational load is greatly reduced. Promising results in both spectral and pitch estimation are shown. Its advantages in efficient speech coding are discussed.