Line spectrum representation of linear predictor coefficients of speech signals

It has been known that the linear predictor coefficients (LPC) of speech signals can be transformed into a “pseudo” vocal-tract area function whose boundary conditions are (a) a complete opening at the lips and (b) a matching resistance termination at the glottis. If the boundary condition at the glottis is replaced by a complete opening or a complete closure, all the poles of the resulting system function will move onto the unit circle in z plane. Using this fact it is possible to describe the original LPCs by two sets of pole frequencies corresponding to the two new boundary conditions at the glottis, or a set of frequency-residue pairs corresponding to either set of poles. These representations have several important features: (1) If an original pole is narrow band, the new pole is close to the original pole; (2) the two sets of pole frequencies alternate and are ordered on the frequency axis; and (3) the problem of locating complex poles can be reduced to solving a polynomial with real roots whose order is one-half that of the original all-pole transfer function.