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GATE 2014 EE (EE1) – Question 36

Signals and Systems · Fourier series representation of continuous and discrete time periodic signals, Sampling theorem · 2 marks · Numerical answer

$g:[0,\infty)\to[0,\infty)$ is $g(x)=x-\lfloor x\rfloor$, where floor denotes the greatest integer not exceeding x. Find the constant term in its Fourier-series expansion.

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Correct answer: 0.5 to 0.5

Explanation

The function g(x)=x−floor(x)is periodic with period1and equals xon0≤x<1. Its constant term is the period average∫₀¹x dx=**1/2=0.5**. If a Fourier convention writes the constant as a0/2, then a0=1but the actual constant term remains0.5.