  Linear prediction (LP) is an ubiquitous analysis method in speech processing.
Various studies have focused on sparse LP algorithms by introducing sparsity
constraints into the LP framework. Sparse LP has been shown to be effective in
several issues related to speech modeling and coding. However, all existing
approaches assume the speech signal to be minimum-phase. Because speech is
known to be mixed-phase, the resulting residual signal contains a persistent
maximum-phase component. The aim of this paper is to propose a novel technique
which incorporates a modeling of the maximum-phase contribution of speech, and
can be applied to any filter representation. The proposed method is shown to
significantly increase the sparsity of the LP residual signal and to be
effective in two illustrative applications: speech polarity detection and
excitation modeling.
