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| + | =Periodic versus non-periodic functions ([[Homework_1_ECE301Fall2008mboutin|hw1]], [[ECE301]])= | ||
| + | <span style="color:green"> Read the instructor's comments [[hw1periodicECE301f08profcomments|here]]. </span> | ||
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== Periodic Functions == | == Periodic Functions == | ||
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] | ||
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| + | 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) | ||
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| + | 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. | ||
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| + | An example of a non-periodic function would be x(t) = e^t | ||
Latest revision as of 06:18, 14 April 2010
Periodic versus non-periodic functions (hw1, ECE301)
Read the instructor's comments here.
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
