Question

The fundamental period of the signal \(x\left( t \right) = 2\cos \left( {\frac{{2\pi t}}{3}} \right) + \cos \left( {\pi t} \right),\) in seconds, is ________s.

Answer 1

\(x\left( t \right) = 2\cos \left( {\frac{{2\pi t}}{3}} \right) + \cos \left( {\pi t} \right)\)

\({T_1} = \frac{{2\pi }}{{\frac{{2\pi }}{3}}} = 3\)

\({T_2} = \frac{{2\pi }}{\pi } = 2\)

Fundamental time period = LCM (T₁, T₂)

= LCM (3, 2) = 6 sec