(→Periodic / Non-Periodic Functions) |
(→Periodic / Non-Periodic Functions) |
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For a function to be continuous in discrete time, it must satisfy <math>a(x+T) = a(x)</math> for any T greater than zero. Furthermore, any continuous time function that does not satisfy the pre-mentioned condition can be deemed non-periodic. | For a function to be continuous in discrete time, it must satisfy <math>a(x+T) = a(x)</math> 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) | + | Ex1: y(t) = cos(t) is periodic |
| − | Ex2: x(t) = e^3t | + | Ex2: x(t) = e^3t is non-periodic |
'''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. | ||
Revision as of 19:58, 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.
