In recent years, faster-Than-Nyquist (FTN) nonorthogonal systems draw more attention for high-capacity communication systems. In this paper, we will introduce digital signal processing for eliminating interference in FTN nonorthogonal systems. FTN non-orthogonal systems can be divided into single-carrier FTN (SC-FTN) and multi-carrier FTN (MC-FTN) non-orthogonal systems. In SC-FTN non-orthogonal systems, joint algorithms will be studied for compensating the serious inter-symbol interference, including joint feed-forward equalizer, post filter and maximum likelihood sequence detection (MLSD) algorithm and joint frequency-domain equalizer and MLSD algorithm. In MC-FTN non-orthogonal systems, intercarrier interference is similar to the interference in multiple input multiple output (MIMO) systems. The interference cancellation algorithm for MIMO systems is also effective for MC-FTN non-orthogonal systems. We will introduce MIMO decoding to eliminate the interference in MC-FTN non-orthogonal systems.