impulse-response

The impulse-response concept (characterizing LTI systems via their response to a Dirac delta input) depends on the concept of signal. Remove the concept of signal and impulse-response loses its domain — signals are what impulse responses describe and process. Without signals as a concept, there is nothing for an impulse response to characterize.

An impulse response is a representational construct: it encodes a system's behavior as a time-domain function. It is not the physical system itself but a map of how the system responds — a human-made representation for analysis and prediction.

Test (SERVES): impulse-response is built and maintained for the sake of measurement — specifically, measuring a system's behavior. An impulse response characterizes a system for measurement purposes. The servant (impulse-response) points at the master (measurement). Law 8d: this records the designed purpose, not a need relation.

Step-response (Heaviside step input characterization) predates and conceptually feeds into impulse-response (Dirac delta input characterization). Which-came-first test: step-response epoch 0.01, impulse-response epoch 0.18. You can derive impulse-response from step-response via differentiation, establishing the conceptual lineage.

An impulse response IS a specific kind of transient response — namely, the transient response to an impulse (delta) input. Law 9: 'X is a specific kind of Y' → INSTANCE_OF. A competent speaker calls an impulse response 'a type of transient response.' Direction: impulse-response → transient-response (specific→general).

Impulse response is a concept that emerged from signal processing theory — it characterizes LTI systems by their response to a Dirac delta input, a notion central to SP analysis. Law 7: signal processing (the broader discipline) existed first and fed into the specific concept of impulse response.

Overshoot is a phenomenon observed when a system's response exceeds its target before settling — it is identified through and derived from the impulse-response (or step-response) of a system. Impulse-response existed first as a characterization method, and overshoot is a property derived from analyzing impulse/step responses.

Transient response of a linear system is characterized by its impulse response — the system's transient behavior is fully described by how it responds to an impulse. Remove impulse response and transient response has no operational characterization in linear systems.

Transient smearing is the temporal spreading of a sharp transient caused by the finite duration and shape of an impulse response. The mechanism is convolution of the transient with the impulse response. Remove impulse-response and the mechanism producing smearing disappears entirely. Direction correct: the artifact (transient-smearing) depends on the mechanism (impulse-response).

Post-ringing is the trailing portion of an impulse response after a transient. Remove the concept of impulse response and post-ringing has no mechanism to describe — it IS a feature of the impulse response.