Question

The fundamental period of the discrete-time signal
$x\left[n\right]=e^{j\left(\frac{5\pi }{6}\right)n}$ is

• A. $\frac{12}{5}$
• B.
  12
• C. $\frac{6}{5\pi }$
• D.
  6

Answer 1

The correct option is B

12
$\text{Given signal is}$

$x\left[n\right]=e^{j\left(\frac{5\pi }{6}\right)n}$

$\text{we can write,}$

$e^{j\left(\frac{5\pi }{6}\right)n}=\cos \left(\frac{5\pi }{6}n\right)+j\sin \left(\frac{5\pi }{6}n\right)$

$\frac{{\omega }_0}{2\pi }=\frac{m}{N}\Rightarrow \frac{m}{N}=\frac{5\pi /6}{2\pi }=\frac{5}{12}$

$\therefore$ $\text{Fundamental period N = 12.}$