# Question:Substituting Periodic Fourier series expansion equation with standing wave equation

## Question:Substituting Periodic Fourier series expansion equation with standing wave equation

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`Substituting Periodic Fourier series expansion equation with standing wave equation`

`Maple formatting cuts off some of the information/question I've included a link to an image of the full questionhttp://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg and as text filehttp://dl.dropbox.com/u/6576402/questions/ques1.txt`
`Greetings AllI can re-create a periodic signal using Fourier series expansion usingsin 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 currentlyexported: 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 offsetVERTOFFaad_1=0; %Vertical offsetAMPmain_1=1; %amplitude increase AMPaaa_1=0; %amplitude increaseFREQmain_1=1; %Frequency increase FREQaab_1=0; %Frequency increase PHASEmain_1=0; %phase shiftPHASEaac_1=0; %phase shiftHere's an link explaining what a standing wave is and it's equation:http://en.wikipedia.org/wiki/Standing_waveHere'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?tiasal22 `
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`Maple formatting cuts off some of the information/question I've included a link to an image of the full questionhttp://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg `
`and as text filehttp://dl.dropbox.com/u/6576402/questions/ques1.txt`
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