Re: Substituting Periodic Fourier series expansion equation
- To: mathgroup at smc.vnet.net
- Subject: [mg118692] Re: Substituting Periodic Fourier series expansion equation
- From: Christopher Arthur <aarthur at tx.rr.com>
- Date: Sat, 7 May 2011 07:33:53 -0400 (EDT)
yourfunction[t_]:= sum of cosines and sines in t;
lengthofperiod = whatever;
Play[yourfunction[t]/maxamplitude,{t,0,lengthofperiod}]
Chris
Rick T a =E9crit :
> Substituting Periodic Fourier series expansion equation with standing
> wave equation
>
>
> the formatting cuts off some of the information/question
> I've included a link to an image of the full question
> http://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg
>
> Greetings All
>
> I can re-create a periodic signal using Fourier series expansion using
> sin and cos waves. But how can I adapt the equation so the equation
> will be outputted in the format of a standing wave equation.
>
> Note: I export the equation in a text format
> Here's an example/format of the equation that is currently
> exported:
>
>
> aa=
> 0.0000000000000000277555756156289135105908+VERTOFFmain_1+VERTOFFaad_1
> +
> ((AMPmain_1+AMPaaa_1)*0.4330127018922191872718485683435574173927)*cos((FREQmain_1+FREQaab_1)*
> 1.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*0.4330127018922194648276047246326925233006)*sin((FREQmain_1+FREQaab_1)*
> 1.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.4330127018922191872718485683435574173927)*cos((FREQmain_1+FREQaab_1)*
> 2.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0000000000000000000000000000000000000000)*sin((FREQmain_1+FREQaab_1)*
> 2.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))));
>
> If your interested here are some of the values I use and what the
> variables mean:
> VERTOFFmain_1=0; %Vertical offset
> VERTOFFaad_1=0; %Vertical offset
> AMPmain_1=1; %amplitude increase
> AMPaaa_1=0; %amplitude increase
> FREQmain_1=1; %Frequency increase
> FREQaab_1=0; %Frequency increase
> PHASEmain_1=0; %phase shift
> PHASEaac_1=0; %phase shift
>
> Here's an link explaining what a standing wave is and it's equation:
> http://en.wikipedia.org/wiki/Standing_wave
>
> Here's another example with more data points showing a
> simple Periodic Fourier series expansion of a sin wave:
>
>
> aa=
> 0.0000000000000000055511151231257830102669+VERTOFFmain_1+VERTOFFaad_1
> +
> ((AMPmain_1+AMPaaa_1)*0.1516614837922138359083135128457797691226)*cos((FREQmain_1+FREQaab_1)*
> 1.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*0.9575529230109556255712277561542578041553)*sin((FREQmain_1+FREQaab_1)*
> 1.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0226651931432310521641326772623870056123)*cos((FREQmain_1+FREQaab_1)*
> 2.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0697562918038196477787948879267787560821)*sin((FREQmain_1+FREQaab_1)*
> 2.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0186918925876187295986863290409019100480)*cos((FREQmain_1+FREQaab_1)*
> 3.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0366849047602344491281201044330373406410)*sin((FREQmain_1+FREQaab_1)*
> 3.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0176163417098331789856224816048779757693)*cos((FREQmain_1+FREQaab_1)*
> 4.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0242468142342565640134921522985678166151)*sin((FREQmain_1+FREQaab_1)*
> 4.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0171650216811894164303797793991179787554)*cos((FREQmain_1+FREQaab_1)*
> 5.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0171650216811893852053572118165902793407)*sin((FREQmain_1+FREQaab_1)*
> 5.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0169359868831254270493680280651460634544)*cos((FREQmain_1+FREQaab_1)*
> 6.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0123047147243315942860553136029011511710)*sin((FREQmain_1+FREQaab_1)*
> 6.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0168085612357091948587672902704071020707)*cos((FREQmain_1+FREQaab_1)*
> 7.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0085643897189793712076966158974755671807)*sin((FREQmain_1+FREQaab_1)*
> 7.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0167362490935154296922693362148493179120)*cos((FREQmain_1+FREQaab_1)*
> 8.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0054379369715433292786777030869416194037)*sin((FREQmain_1+FREQaab_1)*
> 8.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0166987131473295795369704563881896319799)*cos((FREQmain_1+FREQaab_1)*
> 9.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0026448163359797938198880729032680392265)*sin((FREQmain_1+FREQaab_1)*
> 9.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0083435243106618067754354228782176505774)*cos((FREQmain_1+FREQaab_1)*
> 10.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))))
> +
> ((AMPmain_1+AMPaaa_1)*-0.0000000000000000000000000000000000000000)*sin((FREQmain_1+FREQaab_1)*
> 10.0 *(t-(((-PHASEmain_1)+PHASEaac_1)/(FREQmain_1+FREQaab_1))));
>
> Is their a way to adapt/substitute the Periodic Fourier series
> equation
> with the standing wave equation?
>
> tia
> sal22
>
> formatting cuts off some of the information/question
> I've included a link to an image of the full question
> http://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg
>
>
>
