- 2071 Shrawan · 2 marks
Define unit impulse and unit step
Short answer
Unit step u(t)=1 for t≥0, 0 for t<0. Unit impulse δ(t)=0 for t≠0, ∫δ(t)dt=1; it is the derivative of u(t), and sifting property gives ∫x(t)δ(t-t₀)dt = x(t₀).
Define unit impulse and unit step function.
Unit step function u(t): equals 1 for t ≥ 0 and 0 for t < 0.
u(t)
1 | ________
| |
0 +-----+-------> t
Unit impulse function δ(t): zero everywhere except t = 0, where it is infinite, and its total area is one:
δ(t) = 0 for t ≠ 0, and ∫ δ(t) dt = 1.
It is the derivative of the unit step: δ(t) = du(t)/dt. Its sifting property is ∫ x(t) δ(t - t₀) dt = x(t₀).
✓ Answer checked by Claude Opus 5.5 (high effort)
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