Phasenwrap

Phasenwrap is a term used in signal processing to describe the operation of constraining a phase value to a fixed principal interval. In practice, any real-valued phase angle can be wrapped to a bounded range, most commonly between −π and π, or between 0 and 2π. The wrapped phase is a representative of the original angle modulo 2π.

Mathematically, the wrap of a phase θ is often defined as φ = wrap(θ) = θ − 2π floor((θ + π) / (2π)), yielding φ within the chosen principal interval. This operation is surjective but not injective, since all angles differing by integer multiples of 2π map to the same wrapped value. The inverse process is phase unwrap, which seeks to reconstruct a continuous phase by adding back the appropriate multiples of 2π where discontinuities occur.

Implementation considerations include using modulo or remainder operations, with attention to numerical stability near the wrap boundary. When working with arrays or signals, wrapping is applied elementwise. Different applications may use different principal intervals, such as [0, 2π) instead of (−π, π].

Applications of Phasenwrap appear across fields where phase information is central. In interferometry, optics, and radar, wrapped phase data are common and must often be unwrapped for accurate analysis. In communications and control systems, instantaneous phase is routinely wrapped to keep signals within a bounded range. In computer graphics and holography, wrap operations support phase retrieval and visualization tasks.

Overall, Phasenwrap is a standard operation in phase processing that facilitates bounded representation and comparison of phase measurements, while highlighting the need for careful unwrapping in subsequent analysis.