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Terahertz (THz) communication is a highly promising solution for addressing the ultra-high data rate requirements of future sixth-generation (6G) wireless systems. However, the unfavorable frequency-dependent channel characteristics of THz communication pose a significant challenge in realizing this promising technology. In this paper, we present a novel solution to this challenge by proposing a wideband THz system featuring a unique THz-specific digital baseband waveform design tailored to the distinctive channel characteristics of the THz spectrum. To address the frequency-dependent challenges posed by the wideband THz channel and the spectral efficiency loss inherent in conventional orthogonal frequency division multiplexing (OFDM) systems due to cyclic prefix overhead, we propose a THz system with beamforming incorporating a multi-band OFDM (MB-OFDM) based waveform design using a filter-bank based channel model that slices the wideband channel into smaller frequency-independent subbands for ultra-wideband THz communication. Furthermore, this work introduces a novel squint model taking into account the printed-circuit-board (PCB) impairments and circuit imperfections, which have not been considered before. We also propose an all-digital mitigation scheme with this model. We propose a channel estimation algorithm using a three-level adaptive method with an auto-regressive (AR) model for exploiting the frequency dependency among the intra and inter-narrow subbands. Apart from these key contributions, we propose a THz environment-aware precoder to mitigate the wideband effect in the THz channel, specifically the subband-specific path loss and environment-related effect, and balance the overall gains across the band. We have also proposed to optimize the number of subbands and zero-padding in MB-OFDM waveform based on the minimum bit error rate (MBER) criterion. Numerical simulations are carried out to evaluate the performance of the proposed schemes demonstrating their feasibility and effectiveness for wideband THz communication with results showing a lower peak-to-average power ratio (PAPR) for the proposed waveform as compared to conventional OFDM.