Over the past decade, audio coding technology has seen standardization and the development of many frameworks incorporated with linear predictive coding (LPC). As LPC reduces information in the frequency domain, LP-based frequency-domain noise-shaping (FDNS) was previously proposed. To code transient signals effectively, FDNS with temporal noise shaping (TNS) has emerged. However, these mainly operated in the modified discrete cosine transform domain, which essentially accompanies time domain aliasing. In this paper, a unified noise-shaping (UNS) framework including FDNS and complex LPC-based TNS (CTNS) in the DFT domain is proposed to overcome the aliasing issues. Additionally, a modified polar quantizer with phase contrast control is proposed, which saves phase bits depending on the frequency envelope information. The core coding feasibility at low bit rates is verified through various objective metrics and subjective listening evaluations.