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Consider the ...

Question

Consider the signal
$f (t) = 1 + 2 c o s (π t) + 3 s i n (\frac{2 π}{3} t) + 4 c o s (\frac{π}{2} t + \frac{π}{4})$ ,where t is in seconds. Its fundamental time period, in seconds, is ______
12

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Solution

The correct option is A 12
$f (t) = 1 + 2 c o s (π t) + 3 s i n (\frac{2 π}{3} t) + 4 c o s (\frac{π}{2} t + \frac{π}{4})$

$ω_{1} = π$
$ω_{2} = \frac{2 π}{3}$
$ω_{3} = \frac{π}{2}$

$ω_{o} = G C D (π, \frac{2 π}{3}, \frac{π}{2}) = \frac{π}{6}$

Fundamental period,
$N = \frac{2 π}{ω_{o}} = \frac{2 π}{(π / 6)} = 12$

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