fourier transform integration problem

The problem is t(x)=I(0)exp(-a(x)) which is also roughly equal to =I(0)[1-a(x)] but what if we have s(x)=t(xo-m*cos(wt))

find the fourier transform of s(x):

which is given by:

S(y)= int(s(x)*exp(-i*x*y))dx

= int(t(xo-m*cos(wt)*exp(-i*xo*y))dxo

and now is where i get lost the next line in the solution is:

= exp(-i*m*y*cos(wt))*int(t(xo)*exp(-i*xo*y))dxo

i dont understand how they took out the mcos(wt) from the integration, can someone help giving me direction to get to this line before continuing

Re: fourier transform integration problem

Your post is difficult to read. Can you rewrite it using Latex?

Re: fourier transform integration problem

$\displaystyle t(x)=I(0)e^-^a^(^x^) =I(0)[1-a(x)]$

we have we have $\displaystyle s(x)=t(xo-mcos(wt)) $

fourier transform

$\displaystyle \int s(x)e^-^i^x^y dx =\int t(xo-mcos(wt))e^-^i^x^o^y dxo $

$\displaystyle e^-^i^y^m^c^o^s^w^t \int t(xo)e^-^i^x^o^y dxo $ this is the line i am lost line ,i dont understand how they took out the mcos(wt) from the integration, can someone help giving me direction to get to this line before continuing