fasierespons

Fasierespons, commonly referred to as the phase response, describes how the phase of the output signal of a system shifts relative to the input as a function of frequency. It is part of a system's frequency response and complements the magnitude response.

In linear time-invariant systems, the frequency response is H(jω) = |H(jω)| e^{j∠H(jω)}. The phase response is φ(ω) = ∠H(jω). It indicates whether the output lags or leads the input and by how much at each angular frequency ω.

Phase response can be measured by applying sinusoidal inputs at different frequencies and measuring the phase difference, or computed from the system's impulse response via Fourier transform. It is often plotted as a phase plot (sometimes with phase unwrapping to remove 2π jumps) or shown as part of a Bode plot displaying both magnitude and phase.

Key related concepts include phase delay, τ_p = φ(ω)/ω, and group delay, τ_g = -dφ/dω, which describe constant and varying phase shifts with frequency, respectively. A system with the minimum possible phase for a given magnitude is called a minimum-phase system; nonminimum-phase systems exhibit additional phase lag.

Applications span filter design, audio processing, communications, control engineering, and acoustics. For example, a first-order low-pass filter has φ(ω) = -arctan(ωRC), approaching -90 degrees at high frequencies.

Limitations include measurement noise, time delays, dispersion, and nonlinear effects that cause phase distortion. Accurate phase information requires careful calibration and, in data analysis, phase unwrapping to interpret the phase correctly.