The amplitude of the impulse can be scaled by a constant. This is represented by δ(t) → a * δ(t), where 'a' is the scaling factor.
The impulse can be shifted along the time axis. This is represented by δ(t) → δ(t - t0), where 't0' is the amount of shift.
When convolved with another function f(t), it extracts the value of that function at t=0. Mathematically, ∫ f(τ)δ(t-τ)dτ = f(t).
The area under the unit impulse is always 1, regardless of scaling. This is represented by ∫δ(t)dt = 1.
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