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Signals & SystemsPeriodic Signals

A discrete-time sinusoid x[n]=cos(omega0 n) is periodic only if?

  • Aomega0/(2pi) is rational
  • Bomega0/(2pi) is irrational
  • Comega0=1 always
  • DIts amplitude is less than one
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Correct Answer: A. omega0/(2pi) is rational
Explanation: A discrete-time sinusoid is periodic if there exist integers N>0 and k such that omega0 N=2pi k, equivalently omega0/(2pi) is rational.
Reference: Standard signals and systems: periodic signals
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