In various communication systems such as wireless sensor networks, MIMO communications, and cognitive radio, mixed-resolution architectures that incorporate both 1-bit and high- resolution data have proven beneficial. These architectures strike a balance between adhering to physical constraints and achieving significant performance improvements. However, working with mixed-resolution models introduces new challenges in designing estimation and learning methods for the data they produce. The objective of this study, which is the main part of my thesis, is to explore various aspects of a mixed-resolution data system for diverse applications of signal processing algorithms. I am examining challenges at the context of channel estimation, focusing on metrics like MSE estimators and boundaries. The goal is to determine how mixed-resolution observations can be harnessed to create a cost-effective yet highly efficient system.