Re: Question on making a piecewise function periodic tia sal2
- To: mathgroup at smc.vnet.net
- Subject: [mg95274] Re: Question on making a piecewise function periodic tia sal2
- From: dh <dh at metrohm.com>
- Date: Wed, 14 Jan 2009 05:51:36 -0500 (EST)
- References: <gkh0v8$6hk$1@smc.vnet.net>
Hi,
I do not understand fully what you want to do. But, to make a function
periodic is a piece of cake. E.g. if we want some function f to have
period L we may define an operator:
makeper[f_,L_]= f[Mod[#,L]]&
Here is an example. We want a sine with periode: 1:
sin1= makeper[Sin,1]
you may plot the result: Plot[sin1[x],{x,0,3}]
Of course, when you make a function periodic with the wrong periode, you
will get y discontinuity.
hope this helps, Daniel
ratulloch at gmail.com wrote:
> Question on making a piecewise function periodic tia sal2
>
> Greetings All
>
> I'm trying to make a piecewise function look periodic.
> example (shows the positive humps of the sin wave from 0 to 2Pi)
> Manipulate[test=choice[ Piecewise[{{Sin[a*t],t<Pi},{Sin[a*t-Pi]
> +C,t>Pi}}],{t,0,2 Pi}],{a,1,5},{C,0,2},{choice,{Plot,Expand}}]
>
> This command will work if t is 0 to 2 Pi but the sin wave goes
> negative after that I think If I use the Mod command example:
>
> Manipulate[test=choice[ Piecewise[{{Sin[a*t],t<Mod[Pi,4]},{Sin[a*t-Pi]
> +C,t>Mod[Pi,4]}}],{t,0,2 Pi}],{a,1,5},{C,0,2},{choice,{Plot,Expand}}]
>
> It could work so it would never go negative but I'm not sure how to
> implement mod command so the sin wave won=92t go negative. I'm also
> open to other suggestions.
>
> The reason why I'm doing this is that when I do periodic interpolation
> the formula
> Breaks down due to the Gibbs Phenomenon. The signals I'm creating
> have about 200 separate values that=92s why it breaks down. But I'm
> using a simple example to see if it can be done. So I can basically
> stitch multiple simple wave signals together to create one big complex
> one and still have the ability to make the complex signal periodic
> over time.
>
> Tia sal2
>