GATE 2016 EE (EE2) – Question 28

Signals and Systems · Linear time invariant and causal systems · 1 mark · Numerical answer

An LTI system has $H(s)=1/(s+1)$. Input is cos(t) and steady output is $A\cos(t+\alpha)$. The amplitude A is ________.

Show answer and explanation

Correct answer: 0.69 to 0.72

Explanation

At input frequency ω=1 rad/s, $H(j)=1/(1+j)$. Its magnitude is 1/√(1²+1²)=1/√2.

The input amplitude is one, so output amplitude is **0.707107**, within 0.69–0.72. Its phase is −45°, which affects α rather than A.

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