Exercise · ZW-LINEAR-TIME-INVARIANT-SYSTEMS-002 · ★☆☆ Basic
A system is time-invariant if a shift of the input produces:
Choose one option.
Show answer
- A. The same shift in the output
Explanation
Time invariance means that shifting the input shifts the output by exactly the same amount. The other options describe changes that do not occur in a time-invariant system.
Review the concept: Linear time-invariant systems
A linear time-invariant (LTI) system is a system that satisfies superposition and whose behavior does not change when the input is shifted. It is determined by its impulse response \(h[n]\).
\[y[n]=\sum_{k=-\infty}^{\infty} x[k]\,h[n-k]\]
More practice problems: linear time-invariant systems
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-001 Which of these properties is required for a system to be LTI?
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-003 What is the impulse response of an identity system, where y[n]=x[n]?
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-004 A system with y[n]=x[n]^2 is linear.
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-005 Which operation is used to compute the output of an LTI system from its input and its impulse respo…
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-006 If h[n]=δ[n]+δ[n-2] and x[n]=δ[n-1], what is y[n]?
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-007 If h[n]=(tfrac12)^n u[n] and x[n]=δ[n], what is y[2]?
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-008 If x[n]=u[n] and h[n]=δ[n]-δ[n-1], what is y[n]?
- ZW-LINEAR-TIME-INVARIANT-SYSTEMS-009 Let h_1[n]=δ[n]+δ[n-1] and h_2[n]=δ[n-2] be connected in cascade. If x[n]=δ[n], what is the output…
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