- Asked 2/20
- 2072 Kartik · 2+2 marks
- 2071 Chaitra · 2 marks
Define LTI system and impulse response
Short answer
LTI system obeys superposition and time invariance; output is convolution y(t)=x(t)*h(t). Impuse response h(t) is the output for a unit impulse δ(t) with zero initial conditions, fully characterizing the system; e.g., RC low-pass: h(t)=(1/RC)e^{-t/RC}u(t).
Define LTI system and impulse response.
LTI system: a system that is both linear (it obeys superposition: additivity and homogeneity) and time-invariant (a shift in the input produces the same shift in the output). Its output for any input can be found by convolution: y(t) = x(t) * h(t) = ∫ x(τ) h(t - τ) dτ. Examples: RC filters and ideal amplifiers.
Impulse response h(t): the output of a system when the input is a unit impulse δ(t) with zero initial conditions. It completely describes an LTI system: causality requires h(t) = 0 for t < 0, and stability requires ∫|h(t)| dt < ∞. For an RC low-pass filter, h(t) = (1/RC) e^(-t/RC) u(t).
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Output of LTI with h(t) = e^(-at)u(t) and e^(at)u(-t) · Data Communication, chapter 2 · asked 3×
- LTI output for h(t)=e^(-2t), rectangular input · Data Communication, chapter 2 · asked 3×
- LTI output for h(t)=e^(-at)u(t), x(t)=u(t)-u(t-2) · Data Communication, chapter 2
- Unit step response for h(t) = exp(-at) · Data Communication, chapter 2
- Check LTI: y(t) = 2x(t) + 3 · Data Communication, chapter 2
- Stability of h(t) = t·e^(-3t)u(t) · Data Communication, chapter 2
- Frequency response of a CT LTI system · Signals and Systems, chapter 5 · asked 3×
- First-order system impulse and step response · Signals and Systems, chapter 5
- Frequency response; ideal LPF impulse response · Signals and Systems, chapter 5 · asked 2×
- Impulse response; ideal LPF formula · Signals and Systems, chapter 5 · asked 2×