Question

The continuous-time signal x(t) = sin ${\omega }_{0}t$ is a periodic signal. However, for its discrete-time counterpart x[n] = sin ${\omega }_{0}n$ to be periodic, the necessary condition is

• A. $\frac{2\pi }{{\omega }_0}$ to be a ratio of integers
• B. $0\le {\omega }_0<2\pi$
• C.
  none
• D. $\frac{2\pi }{{\omega }_0}$ to be an integer

Answer 1

The correct option is A

$\frac{2\pi }{{\omega }_0}$ to be a ratio of integers

$\text{sin}{\omega }_0\text{n to be periodic}$

$\frac{{\omega }_0}{2\pi }=\frac{m}{N}$

$\text{where m and N both are integers.}$

$\therefore \frac{2\pi }{{\omega }_0}$ will be ratio of integers.