(Question A - Periodic Signals Revisited)
(Question A - Periodic Signals Revisited)
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'''Discrete Time, Non-Periodic:'''  
 
'''Discrete Time, Non-Periodic:'''  
Cos[n] is non-periodic in discrete time whenever it isn't sampled at <math>\pi</math>, <math>2\pi</math>, or <math>\pi/2</math> (or any other multiple of <math>\pi</math>). a[n + T] = a[n] for an integer T.
+
Cos[n] is non-periodic in discrete time whenever it isn't sampled at <math>\pi</math>, <math>2\pi</math>, or <math>\pi/2</math> (or any other multiple of <math>\2pi</math>). In other words, if it doesn't satisfy the equation: a[n + T] = a[n] for an integer T, then it is not periodic.
  
 
'''Discrete Time, Periodic:'''
 
'''Discrete Time, Periodic:'''
 +
Cos[n] is periodic in discrete time when it is sampled in intervals of <math>2\pi</math> ie. <math>\pi</math>, <math>2\pi</math>, or <math>\pi/2</math>.

Revision as of 16:32, 10 September 2008

Question A - Periodic Signals Revisited

I chose to use the CT (continuous time)periodic signal: y(t) = cos(t). The signal can be expressed as both periodic and non-periodic in DT (discrete time).

Discrete Time, Non-Periodic: Cos[n] is non-periodic in discrete time whenever it isn't sampled at $ \pi $, $ 2\pi $, or $ \pi/2 $ (or any other multiple of $ \2pi $). In other words, if it doesn't satisfy the equation: a[n + T] = a[n] for an integer T, then it is not periodic.

Discrete Time, Periodic: Cos[n] is periodic in discrete time when it is sampled in intervals of $ 2\pi $ ie. $ \pi $, $ 2\pi $, or $ \pi/2 $.

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