## Problem A discrete-time signal is defined by the equation: $ x(n) = \cos \left( \frac{\pi }{10} n \right) $ Check if the signal is periodic and, if so, compute its [[fundamental period]] 1. Not periodic 2. 5 3. 20 4. 1/10 5. 10 > [!Solution]- > > Let's check if it is periodic: > $ > \begin{align} > x(n+N) &= \cos\left( \frac{\pi}{10} (n+N)\right) \\ > &= \cos\left( \frac{\pi}{10}n + \frac{\pi}{10}N \right) > \end{align} > $ > Is periodic if > $ > \begin{align} > \frac{\pi}{10}N &= 2 \pi k \\ > N &= 20 k > \end{align} > $ > where $k$ is an integer. The smallest non-zero value for $N$ is $20$. >