phase-response

Phase response is the function φ(ω) mapping frequency to phase shift — remove frequency and the concept has no independent variable and ceases to operate. Removal test passes.

phase-response is a specific kind of frequency-response: while frequency-response broadly describes how a system modifies signal amplitudes across frequencies, phase-response specifically describes the phase shift component. A competent speaker would call phase-response a frequency response.

Phase response is a specific signal-processing concept describing the frequency-dependent phase shift introduced by a system, expressed as the argument (angle) of the complex frequency response H(jω). It is an instance of signal-processing — the discipline of algorithms and methods for analyzing and transforming signals. Sense pinned: phase response as the angular component of frequency response, not the colloquial sense of reacting to something.

Group delay τ_g(ω) = -dφ(ω)/dω — it is the negative derivative of phase response with respect to frequency. Phase response existed first as a concept (mapping frequency to phase shift) and fed into group delay (which maps frequency to delay). Law 7: 'which existed first?' → phase response came first. Historical derivation, not mere dependency.

Phase coherence quantifies consistency of phase relationships across frequency components or over time. Measuring consistency requires a phase response as input; without phase response data, coherence cannot be computed or assessed. Removal of phase response stops phase coherence operation.

Group delay is computed as the negative derivative of phase response with respect to frequency; remove phase response and group delay cannot be calculated or used operationally. Dependency is present-tense operational, not historical.