# Substituting Periodic Fourier series expansion equation with standingwave equation tia sal22

Discussion in 'MATLAB' started by Rick T, May 5, 2011.

1. ### Rick TGuest

Substituting Periodic Fourier series expansion equation with standing
wave equation

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=
+
((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
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=
+
((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

If this is hard to read I've included a link to an image of the
question http://dl.dropbox.com/u/6576402/questions/sub_per_fou_series_expansion.jpg

Rick T, May 5, 2011