(→Periodic / Non-Periodic Functions) |
(→Periodic / Non-Periodic Functions) |
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Ex2: x(t) = e^3t is non-periodic | Ex2: x(t) = e^3t is non-periodic | ||
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''Example 2 is non-periodic because it does not satisfy the requirement a(x+T) = a(x) for T>0.'' | ''Example 2 is non-periodic because it does not satisfy the requirement a(x+T) = a(x) for T>0.'' | ||
Revision as of 05:15, 5 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
Example 2 is non-periodic because it does not satisfy the requirement a(x+T) = a(x) for T>0.
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-periodic
