用驻波方程代替周期傅立叶级数展开方程

Question

我可以使用傅立叶级数展开来重新创建周期信号 正弦波和余弦波。但我怎样才能调整方程 将以驻波方程的格式输出。

格式可能会截断一些信息/问题 我添加了完整问题图片的链接 http://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg 并作为文本文件 http://dl.dropbox.com/u/6576402/questions/ques1.txt

注意：我以文本格式导出方程 这是当前方程的示例/格式 导出：

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))));

如果您对这里感兴趣的是我使用的一些值以及变量的含义：

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

这里有一个链接解释什么是驻波以及我想要替换的方程： http://en.wikipedia.org/wiki/Standing_wave

这是另一个示例，其中显示了更多数据点正弦波的简单周期傅里叶级数展开：

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))));

它们是用驻波方程调整/替代周期傅里叶级数方程的方法吗？

格式可能会截断一些信息/问题 我添加了完整问题图片的链接 http://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg 并作为文本文件 http://dl.dropbox.com/u/6576402/questions/ques1.txt