The synthesis of musical sounds and rendering of sound fields share similar foundations of multidimensional signals and systems. The starting point for sound synthesis is the physical description of a musical resonator (string, drum, bore) and its digital replica. Sound field rendering is based on the acoustic wave equation and the resulting conditions for the propagation of loudspeaker signals. Digital real-time implementations of various methods for sound synthesis and sound field rendering have been topic of numerous projects. A further research topic is the numerical simulation of complex sound fields.