# Talk:Sawtooth wave

WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Importance
Field:  Unassessed

## Relevance to Wikipedia

A plot of RAM usage of the Wikipedia web servers is http://wikimedia.org/stats/live/org.wikimedia.browne.squid.cache.ram.usage.html in the shape of a sawtooth wave]: Memory leaks cause memory use to increase linearly until reboot, at which point it falls to minimum. When this repeats a sawtooth wave is produced.

doesn't seem to happen anymore.
I moved this to talk since it interested me (it doesn't belong in the article regardless, being an example of self-reference). Hyacinth 00:44, 8 Feb 2005 (UTC)

added a more general formula, which matches the illustration at the bottom teadrinker 15:00, 28 March 2006 (UTC)

## rms?

Does anyone know how to calculate the rms amplitude of a sawtooth wave? Adamd1008 (talk) 16:31, 15 June 2008 (UTC)

## References

As it happens, Montgomery and Vaughan have a couple of pages on this, but it still needs improvement. Richard Pinch (talk) 20:46, 28 August 2008 (UTC)

Wofram has a reference page that backs up the MatLab implementation. http://mathworld.wolfram.com/SawtoothWave.html I found the more general function in this article didn't produce the expected sawtooth. The Mathworld version does.

ex. y = x/T - floor(x/T) works but probably needs a phase shift to align with sine. Jdgoettee (talk) 23:09, 21 March 2012 (UTC)

## Sawtooth sound waves

The article does only treat electromagnetical waves. But the sawtooth wave has also great importance in acoustics (for example for synthesizers). But there are some difficulties in translation of EM into sound waves. An inverse sawtooth (starts with a sudden rise in amplitude and then decays linearly) for example would translate into a periodic series of shock waves, if the amplitude is taken as pressure. A translation into a displacement amplitude would not be possible since it would require the air molecules to travel at infinite speed at the vertical section. So how does the air move in a sawtooth sound wave in air? I think this would merit a separte section or subsection in the article.--SiriusB (talk) 09:01, 18 February 2009 (UTC)

As with electromagnetic waves, the transition isn't infinitely sharp, but as sharp as it can be with the given technology. Gah4 (talk) 09:31, 19 February 2009 (UTC)

The article should probably make it clear that some of the descriptions are about idealized waves, not waves as they occur in nature, and not waves as created by electronic equipment. Piano non troppo (talk) 03:13, 20 April 2009 (UTC)

Low-frequency sawtooth waves were used a lot in music from Pokémon Mystery Dungeon (as percussion). But higher-frequency sawtooths are annoying. 68.173.113.106 (talk) 16:01, 4 December 2011 (UTC)

## Sawtooth orientations sound identical

"As audio signals, the two orientations of sawtooth wave sound identical." It's been ages since I messed around with audio waves, but this strikes me as incorrect in at least two ways. Surely it would not be true at low frequencies? If a person can discern a volume change in, say 1/10th of a second, then they would be able to tell a sawtooth from a reverse at 5 cps? If an abrupt rise is always the same as a gradual raise, and an abrupt fall, then wouldn't a square wave sound the same as a sawtooth? (Also, and maybe this is unknown or trivial, since some animals, such as birds, have improved hearing, might an artificially created wave sound appear "strange" to them?) Piano non troppo (talk) 03:13, 20 April 2009 (UTC)

You're correct to question the sentence, as it assumes but does not specify human hearing. 5 cycles isn't something humans would have to worry about, but your point about the lowest frequencies isn't lost. The sentence looks like original research, so if it has no support, then out it goes. Binksternet (talk) 04:28, 20 April 2009 (UTC)

## Application section

There is a lot information in the application section, explaining the technical details of electron beam tracing in CRTs. IMO these do not belong to this article and should be deleted. Stony74 (talk) 14:06, 8 May 2009 (UTC)

## reminder

Is it helpful to add a subject that explains an easy way to construct a sawtooth function, e.g. by using the reminder from a division? — Preceding unsigned comment added by 134.221.172.174 (talk) 07:31, 3 October 2011 (UTC)

## Change de sign

The thirth equation ist incorrect, change the sign on the floor function:

${\displaystyle =2\left({t \over a}-\operatorname {floor} \left({t \over a}+{1 \over 2}\right)\right)}$ — Preceding unsigned comment added by 195.80.218.48 (talk) 19:03, 1 April 2012 (UTC)

## Alternative, simple description of the waveform

Hi. I don't dispute the formula that's present in the article right now. But there is another, very simple, way to describe the sawtooth wave function. This is often found in digital implementations (e.g. in software) but it is not inherently digital.

${\displaystyle f\left(t\right)=t\operatorname {modulo} R}$
This generates a sawtooth waveform with range [0..R).

--Ds13 (talk) 18:05, 4 November 2012 (UTC)

## def by heaviside

the sawtooth wave in terms of the heaviside step function:

${\displaystyle f(t)=a*t*heaviside(t)-a*t*heaviside(t-1)}$ ← a is the amplitude

to become a waveform, f(t)=∑f(t-nT) with n∈ℤ, T the period:

f(t)=∑a*(t-nT)*heaviside(t-nT)-a*(t-nT)*heaviside(t-nT-1)

## Why the (-1)^k ?

That factor just shifts the wave by 1/2 a period and makes a simple idea more complicated, doesn't seem to be needed. 129.55.200.20 (talk) 16:52, 21 December 2012 (UTC)

Maybe because otherwise the equation wouldn't be correct? —Kri (talk) 19:38, 22 December 2012 (UTC)
It would, indeed, be correct, just with a different phase. Check this plot with (-1)^k and this plot without (-1)^k --Leonardo Monteiro Fernandes (talk) 13:12, 2 May 2016 (UTC)

## Sawtooth wave article deletion

hi i'm unsure how to get wiki to ask you. i'll try talk sections.

I'm interested why "solutions to sawtooth wave intersections", which was only a paragraph in length the sawtooth wave article noting places to look for solutions, was deleted.

was there some problem? see below

## Intersection of and Solutions

If a set of un-aligned sawtooth waves all intersect at y==0 for at some x. If only the left side intersections are asked (sloping side), this is the same problem as Chinese remainder theorem.

For two un-aligned waves if an R and L intersect for an x, the solution is the same as inverse modulus. While RR should be easy with LCM.

For other combinations and triangular waves discussion article: