Diamond Algorithm: A Phase Unwrapping Method for Signal Processing

In digital signal processing, phase unwrapping algorithms are methods used to determine the true phase of a signal. These algorithms are commonly applied in signal processing and communication fields such as radar systems, telecommunications, and acoustics. The fundamental principle of phase unwrapping involves converting the wrapped phase (typically constrained within the range of -π to π or 0 to 2π) into a continuously increasing function, making phase variations easier to analyze and process. From a code implementation perspective, this often involves detecting phase jumps by comparing adjacent phase values and adding or subtracting multiples of 2π to maintain continuity. The key advantage of phase unwrapping algorithms lies in their ability to preserve phase continuity even when phase jumps occur, thereby preventing the accumulation of phase errors. Common algorithmic approaches include path-following methods (like Goldstein's algorithm) and minimum-norm solutions. In practical implementations, developers often use functions that scan through phase data, identify discontinuities exceeding π radians, and apply appropriate corrections using modulo operations. Due to these characteristics, phase unwrapping algorithms are particularly valuable in applications requiring high-precision phase measurements, such as interferometric synthetic aperture radar (InSAR), magnetic resonance imaging (MRI), and optical metrology systems. The algorithm typically involves threshold-based discontinuity detection and phase correction loops in its computational structure.