Recently methods for obtaining sparse representations of a signal using overcomplete dictionaries of waveforms have been studied, often motivated by the way the brain seems to process certain sensory signals. Algorithms have been developed using either a specific criterion to choose the waveforms occurring in the representation from a fixed dictionary, or to construct them as part of the method. In the case of speech signals, most approaches do not take into consideration the important temporal correlations that exist; these are known to be well approximated using linear models. Incorporating this type of a priori knowledge of the signal can facilitate the search for a suitable solution and also help with the interpretation of the representation found. In the present paper a method is proposed for obtaining a sparse representation using a generative parametric model. An example, using speech signals, is given reporting the method’s efficacy for different coding costs and sparsity measures.