## Problem Consider the discrete-time signal defined by the equation: $ x(n) = \cos \left( \frac{2\pi }{N} n + \frac{\pi}{4}\right) $ If we want to produce a continuous-time signal with a frequency of $480 Hz$ using a sampling rate of $48 kHz$ what should be the value of $N$? 1. 1/100 2. 1/10 3. 1/1000 4. 100 5. the signal is not periodic > [!Solution]- > > 4. 100 > > The period of the continuous-time signal should be: > $ > T_{0} = \frac{1}{480} s > $ > > Given that the sampling interval is: > $ > T = \frac{1}{48000}s > $ > The period of the discrete-time signal sould be: > $ > N = \frac{T_{0}}{T} = \frac{48000}{480} = 100 > $ >