GATE EE 2014 Set 2 — Question 19
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Signals & Systems → Fourier Analysis & Sampling → Frequency Response
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Question
Consider an LTI system with transfer function If the input to the system is and the steady state output is , then the value of is
Correct answer
(B) 1/15
Solution
To find the steady-state response of the linear time-invariant (LTI) system to a sinusoidal input, we use the frequency response of the system.The transfer function of the system is given by:
Step 1: Find the frequency response
Substitute into the transfer function:Step 2: Evaluate at the input frequency
The input to the system is , which has an angular frequency of .Substituting into :Step 3: Calculate the magnitude
The magnitude of the frequency response at is:Calculate the individual magnitudes:Step 4: Determine the amplitude of the steady-state output
For a stable LTI system, if the input is , the steady-state output is:Here, the input amplitude is . The steady-state output is given as , which can be written in terms of a phase-shifted cosine wave. The amplitude of the output waveform is determined solely by the product of the input amplitude and the magnitude of the transfer function at the operating frequency:Therefore, the value of is .Correct Option: BContinue learning with Success Tracker
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