RTUEE / EC / EEEYr 2024 · Sem 52024

Q6Digital Signal Processing

Question

2 marks

Q.6. Explain causality of a linear time invariant system.

Answer

A linear time-invariant system is causal if its output at any time n depends only on present and past input values, equivalently if its impulse response h(n) = 0 for all n < 0.

A system is causal if the output at any given time n depends only on the input values at the present time and past times (n, n-1, n-2, ...), and not on any future input values. For a linear time-invariant (LTI) system, this condition is equivalent to the requirement that its impulse response h(n) = 0 for all n < 0, since the output is given by convolution y(n) = Σ h(k)x(n-k), and any nonzero h(k) for k < 0 would mean the output at time n depends on the future input value x(n-k) with n-k > n, violating causality.

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