The primary function of a digital signal processor (DSP) is to manipulate and process digital signals for applications such as audio, video, and telecommunications. DSPs convert analog signals into digital form, enabling real-time processing like filtering, compression, and error correction. They are optimized for high-speed mathematical computations, allowing for efficient management of complex algorithms. DSPs are widely used in various devices, including smartphones, hearing aids, and multimedia systems, enhancing audio quality, data transmission, and overall performance of digital communications.