Feature extraction is crucial in intelligent fault diagnosis of rotating machinery. It is easier for convolutional neural networks(CNNs) to visually recognize and learn fault features by converting the complicated one-dimensional (1D) vibrational signals into two-dimensional (2D) images with simple textures. However, the existing representation methods for encoding 1D signals as images have two main problems, including complicated computation and low separability. Meanwhile, the existing 2D-CNN fault diagnosis methods taking 2D images as the only inputs still suffer from the inevitable information loss because of the conversion process. Considering the above issues, this paper proposes a new 1D-to-2D conversion method called Embedding Gramian Representation (EGR), which is easy to calculate and shows good separability. In EGR, 1D signals are projected in the embedding space and the intrinsic periodicity of vibrational signals is captured enabling the faulty characteristics contained in raw signals to be uncovered. Second, aiming at the information loss problem of existing CNN models with the single input of converted images, a double-branch EGR-based CNN, called EGR-Net, is proposed to learn faulty features from both raw signal feature maps and their corresponding EGRs. The bridge connection is designed to improve the feature learning interaction between the two branches. Widely used open domain gearbox dataset and bearing dataset are used to verify the effectiveness and efficiency of the proposed methods. EGR-Net is compared with traditional and state-of-the-art approaches, and the results show that the proposed method can deliver enhanced performance.