Speech recognition in noisy and channel distorted scenarios is often challenging as the current acoustic modeling schemes are not adaptive to the changes in the signal distribution in the presence of noise. In this work, we develop a novel acoustic modeling framework for noise robust speech recognition based on relevance weighting mechanism. The relevance weighting is achieved using a sub-network approach that performs feature selection. A relevance sub-network is applied on the output of first layer of a convolutional network model operating on raw speech signals while a second relevance sub-network is applied on the second convolutional layer output. The relevance weights for the first layer correspond to an acoustic filterbank selection while the relevance weights in the second layer perform modulation filter selection. The model is trained for a speech recognition task on noisy and reverberant speech. The speech recognition experiments on multiple datasets (Aurora-4, CHiME-3, VOiCES) reveal that the incorporation of relevance weighting in the neural network architecture improves the speech recognition word error rates significantly (average relative improvements of 10% over the baseline systems)