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In discrete time, a function is period if there exists an integer N such that x[n+N] = x[n] | In discrete time, a function is period if there exists an integer N such that x[n+N] = x[n] | ||
| − | An example of a discrete time periodic function would be e^(jwn) if and only if w/(2*pi) is a rational number. | + | An example of a discrete time periodic function would be x[n] = e^(jwn) if and only if w/(2*pi) is a rational number. |
In continuous time, a function x(t) is periodic if there exists a T>0 such that x(t+T) = x(t) | In continuous time, a function x(t) is periodic if there exists a T>0 such that x(t+T) = x(t) | ||
| − | An example of a continuous time periodic function would be cos( | + | |
| + | An example of a continuous time periodic function would be x(t) = cos(t) with a period of 2*pi. | ||
== Non Periodic Functions == | == Non Periodic Functions == | ||
All functions that are not periodic I suppose would then be Non-periodic. | All functions that are not periodic I suppose would then be Non-periodic. | ||
| + | |||
| + | An example of a non-periodic function would be x(t) = e^t | ||
Revision as of 15:46, 4 September 2008
Periodic Functions
In discrete time, a function is period if there exists an integer N such that x[n+N] = x[n]
An example of a discrete time periodic function would be x[n] = e^(jwn) if and only if w/(2*pi) is a rational number.
In continuous time, a function x(t) is periodic if there exists a T>0 such that x(t+T) = x(t)
An example of a continuous time periodic function would be x(t) = cos(t) with a period of 2*pi.
Non Periodic Functions
All functions that are not periodic I suppose would then be Non-periodic.
An example of a non-periodic function would be x(t) = e^t
