We show a method to sparsify the speech input that improves the robustness of an automatic speech recognizer. The proposed scheme is added to the system as a preprocessing module prior to the acoustic feature extraction. The preprocessing module passes the input speech signal through a linear predictive (LP) analysis filter and enforces sparsity in the LP residue domain. The sparsified prediction residue finally is filtered to generate the speech signal for computing a sequence of conventional feature vectors used in automatic speech recognition (ASR). Using standard feature vectors, our experiments show that sparsification in LP residue domain improves robustness in ASR performance.