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Inverse Causality and BIBO Stability

Given the following statements for LTI systemsStatement 1:The inverse of a causal LTI system is always causal.Statement 2:If an LTI system is causal, then it is stable.Choose the correct option for the above statements
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Answer & Explanation
Correct AnswerB. Both statements 1 and 2 are false

Quick Explanation

A causal LTI system can have a noncausal inverse: a pure delay is causal, but undoing it requires a time advance. Causality also does not guarantee BIBO stability; stability additionally requires an absolutely integrable/summable impulse response. Therefore both statements are false: option B.

Formula / Key Relation

BIBO stable CT LTI: ∫|h(t)|dt<∞
Inverse Causality and BIBO Stability explanatory diagram

Detailed Explanation

Correct Answer

B — Both statements 1 and 2 are false

Statement-wise Analysis

Statement 1: False

Statement 2: False

Concept and Reasoning

A causal LTI system can have a noncausal inverse: a pure delay is causal, but undoing it requires a time advance. Causality also does not guarantee BIBO stability; stability additionally requires an absolutely integrable/summable impulse response. Therefore both statements are false: option B.

Calculation / Key Relation

BIBO stable CT LTI: ∫|h(t)|dt<∞

Exam Takeaway

Causality, invertibility and stability are separate properties.

Common Mistake

Do not assume the inverse inherits causality or that every causal system is stable.

Quick Trick

Causality, invertibility and stability are separate properties.

Common Mistake

Do not assume the inverse inherits causality or that every causal system is stable.

Exam Tip

Causality, invertibility and stability are separate properties.

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