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Let a causal LTI system be governed by the following differential equation y(t) + 1/4 dy/dt = 2x(t), where x(t) and y(t) are the input and output respectively. Its impulse response is

1. 2e^(-t/4)u(t)
2. 2e^(-4t)u(t)
3. 8e^(-t/4)u(t)
4. 8e^(-4t)u(t)

Correct answer: 8e^(-4t)u(t)

Solution

The equation y + (1/4)dy/dt = 2x becomes dy/dt + 4y = 8x. The transfer function is 8/(s+4), so the impulse response is 8e^(-4t)u(t). This is option 3, not the stored option 0.

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