To make a correct decision during normal and transient states, the signal processing for relay protection must be completed and designated the correct task within the shortest given duration. This paper proposes to solve a dc offset fault current phasor with harmonics and noise based on a Deep Neural Network (DNN) autoencoder stack. The size of the data window was reduced to less than one cycle to ensure that the correct offset is rapidly computed. The effects of different numbers of the data samples per cycle are discussed. The simulations revealed that the DNN autoencoder stack reduced the size of the data window to approximately 90% of a cycle waveform, and that DNN performance accuracy depended on the number of samples per cycle (32, 64, or 128) and the training dataset used. The fewer the samples per cycle of the training dataset, the more training was required. After training using an adequate dataset, the delay in the correct magnitude prediction was better than that of the partial sums (PSs) method without an additional filter. Similarly, the proposed DNN outperformed the DNN-based full decay cycle dc offset in the case of converging time. Taking advantage of the smaller DNN size and rapid converging time, the proposed DNN could be launched for real-time relay protection and centralized backup protection.