group-delay

Relations from this entry

• cmsp693e30480jlssidx7zj9wDEPENDS_ON →

  Group-delay requires frequency-response to operate: τ_g(ω) = -dφ/dω is defined as the negative derivative of the phase component of a frequency-response. Without the frequency-response concept, group-delay is incoherent.

• cmsp693e30480jlssidx7zj9wDERIVED_FROM →

  Group delay was developed as a derived concept from frequency response analysis: τ_g(ω) = -dφ/dω extracts timing information from the phase component of a frequency response. Frequency-response existed as a characterization tool first; group-delay was later derived to describe the temporal consequence of that phase behavior.

• cmsp0eyf803mkjlss1du37wz0DEPENDS_ON →

  Group delay τ_g(ω) = -dφ/dω is the negative derivative of phase with respect to frequency. It fundamentally operates on the concept of phase itself — remove phase and group-delay has no referent. Pinning the sense per Law 11d: we refer to phase (the angular component of a complex signal), not phase-shift (a change in phase).

• cmsp4ey9p041qjlsscqwtm7gfDEPENDS_ON →

  Group delay is operationally defined as the negative derivative of phase-shift with respect to angular frequency. Remove phase-shift and group delay ceases to have any operational definition — it is not a standalone concept but a rate-of-change measure derived from phase-shift behavior.

• cmsph7xoa05c2jlssqqltacp9DERIVED_FROM →

  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.

• cmsppfse7062hjlssc7hsi6avDERIVED_FROM →

  Group delay is defined as the negative derivative of phase spectrum with respect to angular frequency. Phase spectrum existed first as a concept (Fourier decomposition includes phase), and group delay was derived from it as a derived quantity. The which-came-first test passes: phase spectrum is a fundamental FT output; group delay is a derived diagnostic from it.

• cmsps9i0v06eejlssqrjcqyviINSTANCE_OF →

  Group delay is a specific signal-processing concept that measures the time delay of the envelope of a signal's spectral components as a function of frequency, defined as τg(ω) = −dφ(ω)/dω where φ is phase response. It is an instance of signal-processing — the discipline of algorithms and methods for analyzing and transforming signals. Sense pinned: group delay as the derivative-of-phase concept, not the colloquial sense of a delayed group acting.

• cmsph7xoa05c2jlssqqltacp9DEPENDS_ON →

  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.

• cmsps9i0v06eejlssqrjcqyviDERIVED_FROM →

  Group delay is a concept that emerged from signal processing theory — it quantifies the time delay of signal envelopes through LTI systems, a notion that arose within the discipline of signal processing. Law 7: signal processing (the broader discipline) existed first and fed into the specific concept of group delay.

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