Talk:Periodic function

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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 15:35, 22 May 2007 (UTC)

Contents 1 Period of a modified sine graph 2 Help wanted at oscillator 3 Overuse of f for function name 4 Naturally Occuring Functions 5 Constant functions (and one other function)

[edit] Period of a modified sine graph

How do you find the period of a modified sine graph?

What do you mean? The period is the smallest number a such that

f(x+a) = f(x) for all x

i.e. the point at which it starts to repeat itself

What does your modified sine graph look like?

In general, a sine function g(x) = a * sin(m * (x + p)) + d has period P such that m = (2 * Pi) / P. Note that the coefficient of x in (x + p) must be 1. --anon

[edit] Help wanted at oscillator

There is some content at oscillator that needs sorting out. Please read the proposal at Talk:oscillator Cutler 18:51, 18 Feb 2004 (UTC)

[edit] Overuse of f for function name

The function name f is re-used here, sometimes for an arbitrary function and sometimes for a specific one. Would it be clearer if the function that gives the "fractional part" of its argument were named something else? Frac is a reasonably common name for this operation in programming languages. --FOo 02:57, 9 Dec 2004 (UTC)

[edit] Naturally Occuring Functions

Should this secton contain some real-life periodic functions? i.e tides over a 48 hour perion Ac current etc? --anon

[edit] Constant functions (and one other function)

Should constant functions be considered periodic? If f is a constant function, then f(x+p) = f(x) for all p, in which case there is no “smallest” such positive p.

Also, consider the following function of the real numbers:

From

rational + rational = rational

irrational + rational = irrational

it follows that f(x+q) = f(x) for any real number x and rational number q (but again there is no “smallest” such positive q). Should this strange function be considered periodic?

Jane Fairfax 09:58, 12 April 2007 (UTC)

I did not see any requirement on the smallest period in the article. I think these functions are indeed periodic according to the definition. For continuous non-constant functions I think one can prove the existence of the smallest period. For stranger functions, well, we accept them as they are. :) Oleg Alexandrov (talk) 14:49, 12 April 2007 (UTC)

Peter Oliphant: Indeed, I wrote a paper about how periodic functions need not have a smallest period! In fact, I discovered an uncountable number of periodic functions such that they have no smallest period AND they are UNBOUNDED in both the positive and negative directions! This is how. Let I be any irrational number. Then consider the function:

f(x) = a if x = a * I + b [ a,b rational] f(x) = 0 otherwise

This function has every rational as a period, and since 'a' can be as large or as small as desired, the function is unbounded in both the positive and negative directions. THIS is a weird function! Note that the 'otherwise' value need not be '0', but can be ANY real number, and I can be any irrational. Thus, there are an uncountable number of these functions. —Preceding unsigned comment added by 66.166.5.106 (talk) 18:04, 9 February 2009 (UTC)