## 1 Introduction  
Terahertz communications have attracted widespread attention in recent years due to their ultra-high frequency and extremely wide bandwidth [1]. Typically operating in the frequency range of 0.1 to 10 THz, THz systems offer abundant spectrum resources, theoretically enabling transmission rates of hundreds of Gbps to Tbps. Thus, THz communication is considered a key enabler for next-generation wireless systems [2]. However,severe free-space path loss and strong molecular absorption--particularly by water vapor and oxygen--lead to rapid signal attenuation [3, 4, 5, 6, 7, 8]. Additionally, multipath fading and the non-ideal behaviors of high-speed front-end components such as amplifiers, mixers, and antennas introduce significant nonlinear distortion and phase noise [9, 10, 11, 12]. These impairments result in highly distorted and complex channel responses, drastically degrading system performance [13, 14, 15]. Therefore, a powerful equalization technique is critical for reliable THz communications [16]. Conventional channel equalization methods struggle to cope with these challenges. Linear equalizers such as minimum mean square error (MMSE) offer low complexity but fall short in addressing nonlinear impairments such as amplifier saturation and frequency-dependent phase distortion [17]. Nonlinear compensation techniques, such as digital predistortion (DPD), often rely on forward modeling and adaptive feedback, but are difficult to implement efficiently in THz systems due to hardware constraints and rapidly varying channel dynamics [18]. In recent years, with the increasing application of DL in physical-layer communications, many researchers have proposed deep neural network (DNN)-based equalization methods to overcome the limitations of traditional algorithms in modeling accuracy and nonlinear processing [19, 20, 21, 22, 23]. Leveraging the powerful fitting capability of DL, DNNs have become a promising solution for THz systems [24, 25, 26]. Some recent studies have applied DNN-based equalizers to address nonlinear issues in THz links. For instance, [PERSON] et al. proposed a time-frequency domain equalizer (TFDE) based on a 2D convolutional neural network (Conv2D) to mitigate linear and nonlinear impairments in RoF-OFDM systems [27]. [PERSON] et al. introduced an end-to-end waveform-to-waveform auto equalization framework (W2 WAEF) to address similar challenges in seamlessly integrated fiber-THz communication systems [28]. In this work, a two-stage DL equalization method for single-carrier signals in the time-domain is proposed to effectively solve the serious nonlinear distortion problem in terahertz systems. The method hierarchically models the time-domain features of the received signal and realizes the joint compensation of multi-scale nonlinear effects. Specifically, in the first stage, the transmitted and received signals are upsampled to enable high temporal resolution, supporting global feature modeling in the first stage; then, they are downsampled in the second stage to focus on the compact refinement of residual distortion. To the best of our knowledge, this is the first time that this \"coarse-to-fine\" advanced learning strategy is systematically introduced into the equalization framework in a single-carrier terahertz communication system through explicit resolution control (up/downsampling) and stage division. Two DNN models are cascaded to form a complete equalizer to gradually suppress the nonlinearity in the received signal. Compared with the single-stage time-domain equalizer, the proposed two-stage scheme has an increased computational complexity, but significantly improves the processing capability, especially for effectively compensating for the severe nonlinear distortion that is difficult to handle with the single-stage model.