Two periodic signals x(t) and y(t) have the same fundamental period of 3 seconds. Consider the signal z(t) = x(-t) + y(2t+1). The fundamental period of z(t) in seconds is

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1.5

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Solution

The correct option is D
3
$x (- t) \to 3 \to ω_{01} = \frac{2 π}{3}$

$y (2 t + 1) \to \frac{3}{2} \to ω_{02} = \frac{2 π}{3 / 2} = \frac{4 π}{3}$

$ω_{0} = G C D {\frac{2 π}{3}, \frac{4 π}{3}} = \frac{2 π}{3}$

$T = \frac{2 π}{2 π / 3} = 3 sec$

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