Optimal and sub-optimal algorithms for selecting the excitation in linear predictive coders

A generalized coder that includes all types of excitation is presented. In this analysis-by-synthesis scheme, maximization formulae are the same regardless of the kind of excitation. The total excitation is expressed as a linear combination of excitation vectors. Given the number of excitation vectors or, equivalently, the bit rate of the coder, finding the vectors and their corresponding gains is a specific least-squares problem. The standard way this problem is usually solved is given, and three alternative mathematical approaches are proposed. These approaches are a Gram-Schmidt orthogonalization, a Choleski decomposition, a Householder transform. All these procedure have the same geometrical interpretation and lead to the same floating point simulation results