Re: Triangle function

• To: mathgroup at smc.vnet.net
• Subject: [mg14424] Re: Triangle function
• From: John Doty <jpd at w-d.org>
• Date: Wed, 21 Oct 1998 03:32:21 -0400
• Organization: Wampler-Doty Family
• References: <70dctu\$22k@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Andrew Strobel wrote:
>
> Hello,
>
> Has Mathematica got a triangle function where I can choose the frequency
> and the amplitude?
>
> The function is necessary to describe a voltage source. It must be an
> analytical function.
>
> like this:
>
>   /\    /\
> -/--\--/--\---->t
> /    \/    \

Your function isn't analytic at the turning points: it has no second
derivatives.

The simplest expression is probably:

2/Pi*ArcSin[Sin[t]]

However, this is not very tractable.

More conventional, and more tractable, is the Fourier series:

8*Sum[Cos[n*t]/n^2, {n, 1, Infinity, 2}])/Pi^2

replace Infinity with a suitably large odd integer, depending on the

You can also transform the infinite series into a rather inscrutable
"closed form" by evaluating the following (try it):

<<Calculus`FourierTransform`
InverseFourierTransform[
FourierTransform[Sum[8/Pi^2 Cos[n t]/n^2, {n,1,Infinity,2}],t,w],w,t]

This may be good for some purposes.

To adjust frequency and amplitude, multiply "t" by the angular
frequency, and the whole expression by the peak amplitude.

--
John Doty		"You can't confuse me, that's my job." Home: jpd at w-d.org
Work: jpd at space.mit.edu

```

• Prev by Date: Re: FactorInteger
• Next by Date: Re: FactorInteger
• Previous by thread: Re: Triangle function
• Next by thread: Re: Triangle function