Signals & Systems #18 | Systems & Their Properties - LTI Systems
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Learn the 6 fundamental properties that characterize any system! We cover memory, causality, linearity (superposition), time invariance (two-path test), BIBO stability, and invertibility — then test all 6 properties on a concrete example.
Topics covered:
System definition: CT y(t)=H{x(t)}, DT y[n]=S{x[n]}, block diagram notation
Memory: memoryless y(t)=2x(t) vs. memory y[n]=x[n-1], accumulator
Causality: output depends only on present & past — non-causal systems are unrealizable
Linearity: homogeneity + additivity = superposition H{ax₁+bx₂}=aH{x₁}+bH{x₂}
Time Invariance: two-path test — shift input, compare with shifted output
BIBO Stability: bounded input → bounded output; examples of stable and unstable systems
Invertibility: one-to-one mapping, inverse system H⁻¹
Full property test: y[n]=x[n]+x[n-1] — all 6 properties verified → LTI System
ECE 218-based Signals & Systems series.
Lecture 8 — Part 2 of 2.
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