MATLAB Implementation of Digital Phase-Locked Loop (DPLL) with Algorithm Explanation

This MATLAB implementation provides a functional digital phase-locked loop (DPLL) system designed for phase and frequency synchronization applications. The code architecture includes three core components: a phase detector for error calculation, a loop filter for noise reduction and stability, and a numerically controlled oscillator (NCO) for generating synchronized output signals. Key implementation features include: - Configurable loop bandwidth parameters for different locking requirements - Discrete-time processing with sampling rate adaptation - Phase error computation using multiplier-based or XOR-based detection methods - Proportional-integral (PI) loop filter design for optimal transient response - Direct digital synthesis (DDS) approach for NCO implementation The algorithm employs a feedback control system that continuously adjusts the NCO frequency to minimize phase difference between input and output signals. Practical applications include carrier recovery in communication systems, clock synchronization in digital circuits, and demodulation of frequency-modulated signals. For enhanced usability, the code includes parameter tuning guidelines, performance analysis sections, and comparative examples showing different DPLL configurations. Alternative implementation approaches such as software-based Costas loops or ZC-DPLL (Zero-Crossing Digital Phase-Locked Loop) architectures are discussed with respective advantages in noise immunity and implementation complexity.