phasemeasuring

Phasemeasuring is the process of extracting and quantifying the phase component of a signal. It is central whenever phase carries meaningful information, such as in coherent demodulation, interferometry, and vibration analysis.

Definition and representations: A real signal x(t) can be represented by its analytic signal x_a(t) = A(t) e^{jφ(t)}, where A(t) is instantaneous amplitude and φ(t) is instantaneous phase. The phase is often obtained from the complex representation of the signal in the frequency domain or via the Hilbert transform.

Methods: Fourier-based phase extraction uses the angle of the spectrum to obtain phase across frequencies. Hilbert-transform-based methods compute φ(t) = arctan(H{x}(t)/x(t)) to form the analytic signal. Phase unwrapping removes 2π discontinuities to produce a continuous phase function. Phase differences Δφ = φ_x − φ_y quantify relative phase between channels, and group delay = −dφ/dω describes how phase varies with frequency. In practice, windowing and nonstationarity affect estimates, and noise can degrade accuracy.

Applications: In communications, phase measurements enable coherent demodulation and phase-locked loops. In optics, phase retrieval and interferometry rely on accurate phase information. Other uses include ultrasound and seismic imaging, structural health monitoring, and various forms of audio processing where phase coherence matters.

Challenges: Key issues include noise susceptibility, phase wrapping, reference selection, and nonstationary signals which require robust estimation strategies.

See also: phase, analytic signal, Hilbert transform, phase unwrapping, cross-spectral density, group delay, coherence.