In this paper, we propose Discriminative Collaborative Representation (DCR) as an extension to Collaborative Representation (CR), by adding an extra discriminative term to the original formulation of CR. In the literature, both CR and Sparse Representation (SR) have been shown to be good in signal classification. Compared to SR, CR is more computationally efficient, but does not give obvious performance improvement. Therefore, we propose DCR, which aims at improving the performance of CR in signal classification. Besides, we extend DCR to Kernel DCR (KDCR), which generalizes DCR by introducing kernel functions. Comparisons among SR, CR and DCR are made in doing two audio signal classification tasks. Experimental results show that DCR can outperform CR and SR in both classification tasks, which demonstrates the effectiveness of our proposed DCR and the usefulness of the extra discriminative term.