Question

If a continuous-time signal x(t) = cos(2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is
1. -0.707
2. -1
3. 0
4. 1

Answer 1

Correct Answer - Option 3 : 0

Given that, x(t) = cos (2πt)

Sampling frequency = 4 Hz

Time period (T) = ¼

replace t = nT_s

Discrete time sequence

x(n) = x(nT_s)

\(= \cos \left( {2\pi \times \frac{n}{4}} \right)\)

\(= \cos \left( {\frac{{n\pi }}{2}} \right)\)

\({\rm{at\;n}} = 5,{\rm{\;x}}\left( {\rm{n}} \right) = \cos \left( {\frac{{5\pi }}{2}} \right) = 0\)