Fourier Series

[XL-power]

hi all,,

i have a simple question but my memory is stick with it
so could you please help me
i want to find the Fourier series for the following function

f(x)={Acos(ωt) where 0<ωt<π
-Acos(ωt) where-π<ωt<0}

i tried several times and the answer is zero?

 

[MrAl]

Hi,


You may have to restate your question. Do you mean cos(w1*t) and cos(w2*t) or what?
Or are you saying that when the first wt is 0 the second wt is -pi, and they are sync'd in time
so that later when the first wt is pi the second wt is 0 ?

Note that cos(-x)=cos(x) too.
Note also that cos(pi/4) does not equal cos(-pi*3/4).

 

[XL-power]

Hi,


You may have to restate your question. Do you mean cos(w1*t) and cos(w2*t) or what?
Or are you saying that when the first wt is 0 the second wt is -pi, and they are sync'd in time
so that later when the first wt is pi the second wt is 0 ?

Note that cos(-x)=cos(x) too.
Note also that cos(pi/4) does not equal cos(-pi*3/4).

thanks for your reply
actually i don't know if i understand your point, what i mean is that the function is f(x)=absolute of (Acos(ωt) )
and the period is 2pi

 

[MrAl]

Hi again,

Are you now saying your function is to take the absolute value of Acos(wt)?
And maybe you are trying to use two waves to get the abs(Acos(wt))? In which case you would do each part separately and add later, probably using a time shift.

For Acos(x1)-Acos(x2) where x1 goes from 0 to pi and x2 goes from -pi to 0, you could probably substitute and do this:
y=Acos(x1)-Acos(x1-pi)

Im still not sure i understand you yet though.

 

[XL-power]

Hi again,

Are you now saying your function is to take the absolute value of Acos(wt)?
And maybe you are trying to use two waves to get the abs(Acos(wt))? In which case you would do each part separately and add later, probably using a time shift.

For Acos(x1)-Acos(x2) where x1 goes from 0 to pi and x2 goes from -pi to 0, you could probably substitute and do this:
y=Acos(x1)-Acos(x1-pi)

Im still not sure i understand you yet though.

yes it's right understanding
so i can do Acos(x1)-Acos(x2) where x1 goes from 0 to pi and x2 goes from -pi to 0

 

[misterT]

Maybe this helps: Fourier Series for Rectified Sine Wave