Revision as of 20:56, 4 September 2008 by Longja (Talk)

Periodic Signal Definition

  • For a Continuous-time signal
     There exists a positive value of T for which
     
     $ x(t) = x(t - T) $
     
     for all values of t.
  • For a Discrete-time signal
     There exists a positive integer N for which
     
     $ x[n] = x[n + N] $
     
     for all values of n.
     
     Note: N is the period of the signal.


Problems

  • Periodic Continuous-Time Signal
     $ x(t) = 3\cos(4t + \frac{\pi}{3}) $
     
     
     As you can see in graph the signal is being repeated and a value T can be used to get the same value during other times of the signal. 
  • Not Periodic Discrete-Time Signal
     $ x[n] = \cos(\frac{\pi}{8}n^2) $


  • Bonus Question


     $ x(t) = e^{j(\pi t-1)} $
     
     
     
     Is periodic, when graphed it produces a straigh line. 
     Since it is a line, at any time the value of the signal will be equal to any other time.



    Credit: Problems were taken from Signals & Systems 2nd ed. (Oppenheim)  Page 61

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