In continuous-time signal classification, the Dirac delta δ(t) is best described as which type of signal?

Introduction / Context:
The Dirac delta δ(t) is a generalized function (distribution) frequently used to model impulsive events and ideal sampling. Classifying it within the conventional energy/power framework highlights important distinctions between ordinary signals and distributions used in system theory.

Given Data / Assumptions:

• δ(t) is the unit impulse with ∫{−∞}^{∞} δ(t) dt = 1.
• Energy is E = ∫ |x(t)|^2 dt; average power is P = lim{T→∞} (1/(2T)) ∫_{−T}^{T} |x(t)|^2 dt.

Concept / Approach:
For ordinary signals, finite energy implies zero average power, and periodic power signals have infinite energy but finite average power. However, δ(t) is not a classical function; |δ(t)|^2 is not defined in the usual sense, so E and P are not finite, nor meaningfully defined. Thus δ(t) is neither an energy signal nor a power signal in the traditional sense used for LTI analysis.

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