1. An apparatus that is configured for dynamic normalization to reduce loss in precision for low-level signals, comprising: a processor; memory in electronic communication with the processor; and instructions stored in the memory, the instructions being executable to: determine a normalization factor for a current frame of a signal, wherein the current frame comprises M bits, wherein the M bits comprise N most significant bits and M-N least significant bits, wherein the M-N least significant bits of the current frame are discarded, wherein the normalization factor depends on an amplitude of the current frame of the signal, and wherein the normalization factor also depends on values of filter states of a high band excitation generator after one or more operations were performed on a previous frame of a normalized low band excitation signal; normalize the current frame of the signal based on the normalization factor that is determined, wherein the normalized current frame utilizes more of the N most significant bits than the current frame; and adjust the filter states' normalization factor based on the normalization factor that is determined.