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 minimumphase. 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.