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