Re: ï

• To: mathgroup at smc.vnet.net
• Subject: [mg95620] Re: ï
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 22 Jan 2009 07:15:12 -0500 (EST)
• Organization: Uni Leipzig
• References: <gl722n\$cai\$1@smc.vnet.net>

```Hi,

because your Piecewise[] functions are not periodic, i.e.,
the interval where the piece is defined is not Mod[_,somePeriod]

Regards
Jens

ratulloch at gmail.com wrote:
> Why isn't the increase in frequency/periodicity of this waveform not
> showing up tia sal2
>
> Greetings All
>
> I'm using the manipulate command to view what the wave form will look
> like will look like if I increase the frequency.
> But when I vary the variable =A1=A7a=A1=A8  to 3 the waveform only shows one
> complete wave instead of 3
>
> Example I vary the variable =A1=A7a=A1=A8 to 3 it should show 3 waveforms
> repeating but instead it shows just 1 waveform in 1/3 the time.
>
> Here=A1=A6s an image of what it's doing along with the code
> http://test.onewithall.net/math/waveform.jpg
>
> Here's the code below:
>
> tmin:=0
> tmax:=2 Pi
> per1=Pi;
> startPer1=0;
> fpr1[t_]:={Sin[Mod[t-startPer1,per1]+startPer1],startPer1<t<per1}
>
> per2=2 Pi;
> startPer2=Pi;
> fpr2[t_]:={.3*Sin[Mod[t-startPer2,per2]+startPer2],startPer2<t<per2}
>
> Manipulate[test=choice[Piecewise[{fpr1[(a*2 Pi)*(t-(phase/360/a))],fpr2
> [(a*2 Pi)*(t-(phase/360/a))]+c}],{t,tmin,tmax}],{{tmax,1,"t Time
> Scale"},0,5 Pi,1,Appearance=84_"Labeled"},{{a,1,"a Repeat Signal CPS"},
> 0,1000,1,Appearance=84_"Labeled"},{{phase,0,"Phase in degrees"},
> 0,-360,.5,Appearance=84_"Labeled"},{{c,0,"Offset C"},
> 0,-294,1,Appearance=84_"Labeled"},{choice,{Plot,Expand}}]
>
> 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 thats 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 increase the frequency of the complex signal
> over time.
>
> Is there another way I should be doing this?  I'm open to all
> suggestions
>
> Tia sal2
>

```

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