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What is the even part of the signal x(t) = 2 + cost ?

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HPCL Engineer Instrumentation 11 Aug 2021 Official Paper
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  1. 2 + sin t
  2. 2cos t
  3. 2 - sin t
  4. 2 + cos t

Answer (Detailed Solution Below)

Option 4 : 2 + cos t
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Detailed Solution

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Solution

Any signal is made up of even and odd part

x(t) = x even (t) + x odd (t)

  • The even part of any signal is given by
  • x even (t) = \(\frac{x(t) + x(-t)}{2}\)
  • The odd part of the signal is given by 
  • x odd (t) = \(\frac{x(t) - x(-t)}{2}\)

Calculation

We have x(t) = 2 + cost 

x even (t) = \(\frac{(2+cost) + (2+cos(-t))}{2} \)

Since cos(-t) = cos(t)

We have, x even (t) = 2 + cost

Hence the correct answer is option 4

 

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