Modeling, Estimation and Optimal Filtration in Signal Processing

Appendix D

From AR Parameters to Line Spectrum Pair

In this appendix, we recall the alternatives to the AR modelling, such as those based on log area ratio functions. These functions ensure that the system is stable even after quantification. We also recall other alternatives such as the “line spectrum pairs” (LSP) and the “immitance spectrum pairs” (ISP), both of which are widely used in speech coding standards. We also consider the cepstrum coefficients and the linear prediction cepstrum coefficients (LPCC), both essentially used in speech recognition.

In the field of speech coding, if the AR parameters obtained using the Yule-Walker equations are transmitted, they have to be quantified by a sufficiently high number of bits, generally about ten, to ensure the exact fit of the spectral envelope of the signal under analysis. Nonetheless, the calculation cost of this procedure is quite high. Due to this high cost, an alternative approach, called the Durbin-Levinson algorithm, is often adopted.

The PARCOR reflection coefficients are less sensitive to quantification. To further lower this sensitivity, we can also use the log area ratio functions defined as follows:

These coefficients can be understood as the bilinear transformation of the reflection coefficients ρ_i. It should be noted that the reflection coefficients can be expressed in terms of the elements LAR_i with a hyperbolic ...