Question

**5. The sinusoidal signal cos(ω0n + θ0) is periodic in n
if the normalized frequency f0 ω0 2π is a rational number, that is,
f0 = MN , where M and N are integers.**

**(a) Prove the above result.**

**(b) Generate and plot (use the stem function)
cos(0.1n−π/5), −20 ≤ n ≤ 20. Is this sequence periodic? Can you
conclude periodicity from the plot?**

**(c) Generate and plot (use the stem function) cos(0.1πn
− π/5), −10 ≤ n ≤ 20. Is this sequence periodic? If it is, what is
the fundamental period. What interpretation can you give to the
integers M and N ?**

Answer #1

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