Periodic versus non-periodic functions (hw1, ECE301)

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Periodic functions

A periodic function is a function whose values repeat at regular intervals. Given an interval of length t, and a function f, if the value of the function at x + t is equal to the value of the function at x then f is a periodic function. In standard function notation this is written f(x + t) = f(x) (read "f of x plus t equals f of x"). The shortest length t for which the function repeats is called the period of the function. The number of times a function repeats itself within a fixed space or time is called its frequency. The maximum value of the function is called the amplitude of the function. When the graphs of two functions having the same period and frequency repeat at different values of the independent variable (x), they are said to be phase shifted or out of phase, and the difference is called the phase angle.

Non-Periodic Functions

An aperiodic function (non-periodic function) is one that has no period which repeats itself (not to be confused with an antiperiodic function for which f(x + P) = −f(x) for some P).

Refrences Books

Abbot, P., and M. E. Wardle. Teach Yourself Trigonometry. Lincolnwood, IL: NTC Publishing, 1992.

McKeague, Charles P. Trigonometry. 3rd ed. Fort Worth, TX: Saunders College Publishing, 1994.

Pierce, John R. Almost All About Waves. Cambridge, MA: MIT Press, 1981.

Swokowski, Earl W. Pre Calculus, Functions, and Graphs. Boston: PWS-KENT Publishing, 1990.