Digital Signal Processors (DSP) are electronics component that converts Analog/Digital signal to IP packets and vice versa. These reside on phones that does the conversion. They also reside on Voice gateways. Voice Gateways are routers on which PSTN/service provider lines are terminated. These lines are often analog (if it is CO line) or Digital (if it is T1/E1). The gateway will also have an ethernet interface. The DSPs will convert the PSTN signaling and protocol stack to IP signaling and protocol stack. They also aid in call conferencing, transcoding and compressing voice packets.
For more information to DSPs please visit DSP tutorial