This paper develops an explainable deep learning model that estimates the remaining useful lives of rotating machinery. The model extracts high-level features from Fourier transform using an autoencoder. The features are used as input to a feedforward neural network to estimate the remaining useful lives. The paper explains the model's behavior by analyzing the composition of the features and the relationships between the features and the estimation results. In order to make the model explainable, the paper introduces octave-band filtering. The filtering reduces the input size of the autoencoder and simplifies the model. A case study demonstrates the methods to explain the model. The study also shows that the octave band-filtering in the model imitates the functionality of low-level convolutional layers. This result supports the validity of using the filtering to reduce the depth of the model.