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Response Functions & Signal Analysis

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Abstractions about how systems respond to and transform signals, including causal response-function relations (Kramers-Kronig relations, dissipation factor, semilinear response), simulation and stability methods for wave and field equations (pseudospectral time-domain method, Von Neumann stability analysis), and frequency-domain filtering and feedback representation (log Gabor filter, causal loop diagram).

7 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

  • Causal loop diagram — Map hypothesized causal influence among changing variables with signed arrows and closed reinforcing or balancing loops, providing a qualitative feedback model whose links require narrative, boundary, and evidence.
  • Dissipation factor — Express oscillatory loss as the ratio of dissipative to reactive response, equivalently the reciprocal of quality factor under a declared convention.
  • Kramers–Kronig relations — Hilbert-transform relations connecting real and imaginary parts of a causal linear response function through analyticity in the upper complex-frequency half-plane.
  • Log Gabor filter — A band-pass signal filter whose transfer function is Gaussian on a logarithmic frequency axis, providing no DC component and flexible bandwidth for localized multi-scale analysis.
  • Pseudospectral time-domain method — A wave-simulation method that computes spatial derivatives through global spectral transforms while advancing the field on a discrete time grid.
  • Semilinear response — A mesoscopic response framework in which energy absorption depends on the connected percolation of driven transitions through a sparse network in energy space rather than on their simple arithmetic average.
  • Von Neumann stability analysis — A Fourier-mode method for testing linear finite-difference schemes by requiring their amplification factors not to grow beyond the stability bound.