My PhD dissertation focused on speech separation, a task that isolates a target speech from background noise (speech enhancement) or other interfering speakers (speaker separation). Speech processing is inherently a sequential task, making it a natural fit for neuromorphic computing, which excels in processing sequential data efficiently. While the human auditory system excels at speech separation, replicating this ability in artificial systems has proven challenging. Enhancing speech quality and intelligibility is a primary goal in speech separation tasks. To achieve this, I proposed integrating human speech elements into waveform-based deep neural networks (DNNs). This approach has proven to be a simple yet effective strategy for improving speech performance. My dissertation introduces three key solutions to effectively incorporate these human speech elements into waveform speech separation models. At the end of my PhD, our lab initiated an SNN project, and attending lectures on the topic sparked my interest in neuromorphic computing, motivating me to pursue related postdoctoral research.