Discrete-time systems are processes that operate on signals at specific intervals, rather than continuously. In these systems, data is sampled at distinct time points, allowing for easier analysis and manipulation. For example, a digital audio recording captures sound waves at regular intervals, converting them into a format that can be processed by computers. These systems are essential in various fields, including signal processing, control systems, and communications. By using mathematical tools like Z-transforms, engineers can analyze and design systems that respond predictably to inputs. This makes discrete-time systems crucial for developing technologies such as digital filters and microcontrollers.