alleryStart learning →A discrete-time signal x[n] = cos(Ω₀·n) is periodic in n if and only if Ω₀/(2π) is which?
AStrictly between 0 and 1 in the real line only
BAny irrational positive real number whatsoever
CA rational number m/N with integer m, N
DEqual to exactly π/2 under every condition only
Answer & Solution
Correct answer: C. A rational number m/N with integer m, N
x[n] periodic with period N iff Ω₀·N = 2π·m for integers m, N, i.e. Ω₀/(2π) rational.
Irrational Ω₀/(2π) gives aperiodic discrete cosine (Oppenheim Ch.1).
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