Neural Radiance Field (NeRF) methodologies have garnered considerable interest, particularly with the introduction of grid-based feature encoding (GFE) approaches such as Instant-NGP and TensoRF. Conventional NeRF employs positional encoding (PE) and represents a scene with a Multi-Layer Perceptron (MLP). Frequency regularization has been identified as an effective strategy to overcome primary challenges in PE-based NeRFs, including dependency on known camera poses and the requirement for extensive image datasets. While several studies have endeavored to extend frequency regularization to GFE approaches, there is still a lack of basic theoretical foundations for these methods. Therefore, we first clarify the underlying mechanisms of frequency regularization. Subsequently, we conduct a comprehensive investigation into the expressive capability of GFE-based NeRFs and attempt to connect frequency regularization with GFE methods. Moreover, we propose a generalized strategy, G2fR: Generalized Grid-based Frequency Regularization, to address issues of camera pose optimization and few-shot reconstruction with GFE methods. We validate the efficacy of our methods through an extensive series of experiments employing various representations across diverse scenarios.