Periodic versus non-periodic functions (hw1, ECE301)

Read the instructor's comments here.

Periodic Functions

A Periodic Function is a function where the entire graph is formed from copies of a particular portion at specified intervals.

The Function :$ f(x) = sin(x)\,\! $ is a periodic function with a Period :$ T = 2*\pi\,\! $.

This sine wave function repeats itself every period of :$ 2*\pi,\! $

Periodic function $ f(x) = sin(x) $. The graph consists of copies of the values $ T = 0 $ to $ T = 2*\pi $.

Non-Periodic Functions

The Function :$ f(x) = cos(e^x)\,\! $ is non-periodic since the graph does not consist of copies of one part of the graph positioned one after the other.

Non-Periodic function $ f(x) = cos(e^x) $. The graph has no visible repeated copies of one part of the graph.


Sources

http://en.wikipedia.org/wiki/Periodic_function

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Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

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