(→Periodic / Non-Periodic Functions) |
(→Periodic / Non-Periodic Functions) |
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== Periodic / Non-Periodic Functions == | == Periodic / Non-Periodic Functions == | ||
| − | CONTINUOUS TIME (CT) | + | '''CONTINUOUS TIME (CT)''' |
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. | ||
| − | DISCRETE TIME (DT) | + | Ex1: y(t) = cos(t) is periodic |
| + | |||
| + | ''Example 1 is periodic since it satisfies the requirement a(x+T) = a(x) for T>0.'' | ||
| + | |||
| + | 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 <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. | ||
| + | |||
| + | Ex1: y[n] = 1 is continuous | ||
| + | |||
| + | Ex2: x[n] = cos[n] is non-periodic | ||
Latest revision as of 05:16, 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
Example 1 is periodic since it satisfies the requirement a(x+T) = a(x) for T>0.
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
