(Periodic / Non-Periodic Functions)
(Periodic / Non-Periodic Functions)
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'''DISCRETE TIME (DT)'''
 
'''DISCRETE TIME (DT)'''
 
For a function to be continuous in discrete time, it must satisfy <math>a[n+T] = a[n]</math> for an integer T.  If these conditions are not met, then it is deemed non-periodic.  Furthermore, both sin and cosine are non-periodic in discrete time.
 
For a function to be continuous in discrete time, it must satisfy <math>a[n+T] = a[n]</math> for an integer T.  If these conditions are not met, then it is deemed non-periodic.  Furthermore, both sin and cosine are non-periodic in discrete time.
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Ex1: y[n] = 1 is continuous
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Ex2: x[n] = cos[n] is non-period

Revision as of 20:00, 4 September 2008

Periodic / Non-Periodic Functions

CONTINUOUS TIME (CT) For a function to be continuous in discrete time, it must satisfy $ a(x+T) = a(x) $ for any T greater than zero. Furthermore, any continuous time function that does not satisfy the pre-mentioned condition can be deemed non-periodic.

Ex1: y(t) = cos(t) is periodic

Ex2: x(t) = e^3t is non-periodic

DISCRETE TIME (DT) For a function to be continuous in discrete time, it must satisfy $ a[n+T] = a[n] $ for an integer T. If these conditions are not met, then it is deemed non-periodic. Furthermore, both sin and cosine are non-periodic in discrete time.

Ex1: y[n] = 1 is continuous Ex2: x[n] = cos[n] is non-period

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