Vibration signals are widely utilized in many fields, which can reflect machine health state. Those typical deep learning techniques cannot learn impulsive features from vibration signals due to interference of strong background noise. Supervised learning greatly rely on vast labeled data, which limits the implementation of deep learning in industry applications. Hence, in this article, a new deep neural network (DNN), sparse representation convolutional autoencoder (SRCAE), is proposed to extract impulsive components of vibration signals for machinery fault diagnosis in an unsupervised manner. A sparse representation (SR) block is proposed to extract impulsive components of vibration signals and transform the time-domain signal to a sparse domain by sparse mapping of a convolutional graph. The SR block is inserted into a deep network to remove noise and learn impulsive features for machinery fault diagnosis. Furthermore, an unsupervised selective feature transmission mechanism is proposed to improve training efficiency and realize feature filtering simultaneously. Finally, the effectiveness of SRCAE is verified on rotary machine fault diagnosis experiments. The testing results show that SRCAE has good noise filtering and impulsive components extraction performance. The recognition accuracy of SRCAE reached 97.16% based on the fivefold cross validation, which demonstrates the outperformance of SRCAE in comparison with state-of-the-art DNNs.