Phaseninvarianz

Phaseninvarianz refers to a property of certain systems or transformations where the phase information of a signal or wave remains unchanged. In the context of signal processing, a system exhibits phaselocked behavior if the phase difference between its input and output signals is constant over time, regardless of amplitude variations. This is often a desirable characteristic in applications like communication systems and control systems where maintaining the relative timing of signals is crucial.

In wave phenomena, phaselocked means that two or more waves are oscillating with a constant phase difference. This can occur naturally or be induced by external forces. For instance, in laser physics, multiple lasers can be phase-locked to produce a combined beam with enhanced coherence and power. In the study of coupled oscillators, phase-locking is a common emergent behavior.

Mathematically, phaselocked behavior can be described by stating that the phase difference, phi, between two signals, x(t) and y(t), satisfies d(phi)/dt = 0, where phi(t) = phase(y(t)) - phase(x(t)). This implies that phi(t) is a constant, say phi_0.

The concept of phaselocked is distinct from frequency locking, although frequency locking often implies phase locking. If two signals are frequency locked, their frequencies are equal or harmonically related. If they are also phase locked, their phase difference is constant. Understanding phaselocked behavior is important in various scientific and engineering disciplines, including physics, electrical engineering, and mechanical engineering, for analyzing and controlling oscillatory systems.