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GATE 2014 EC (EC1) – Question 42

Networks, Signals and Systems · Continuous-time Signals · 2 marks · Numerical answer

The figure shows periodic x as a function of time. Find its rms value.

Diagram for GATE 2014 EC (EC1) question 42

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Correct answer: 0.39 to 0.42

Explanation

During the first half-period x(t)=2t/T and during the second half x=0. Hence x_rms²=(1/T)∫₀^(T/2)(2t/T)²dt=1/6. Taking the square root gives **1/√6=0.408248**. The zero interval must be included when averaging over a full period.