Question

Which of the following is correct about the signal ?

$x\left(t\right)=\sin \left(\frac{\pi }{10}t\right)+\sin \left(\frac{\pi }{7}t\right)+\cos (\frac{9\pi }{7}t+{30}^{\circ })$

• A. It is periodic with period 630
• B. It is periodic with period 180
• C. It is periodic with period 140
• D. It is non-periodic

Answer 1

The correct option is C It is periodic with period 140

$T_1=\frac{2\pi }{\left(\frac{\pi }{10}\right)}=\frac{20}{1}$

$T_2=\frac{2\pi }{\left(\frac{\pi }{7}\right)}=\frac{14}{1}$

$T_3=\frac{2\pi }{\left(\frac{9\pi }{7}\right)}=\frac{14}{9}$

$T=\frac{LCM(20,14,14)}{GCD(1,1,9)}=\frac{140}{1}=140$