- #1
jjr
- 51
- 1
Hello
I am trying to determine the Fourier transform of the hyperbolic tangent function. I don't have a lot of experience with Fourier transforms and after searching for a bit I've come up empty handed on this specific issue.
So what I want to calculate is:
##\int\limits_{-\infty}^\infty e^{-it\omega}\text{tanh}(bt) dt##
where ##b## is some constant.
Using ##\text{tanh}(bt)=\frac{e^{bt}-e^{-bt}}{e^{bt}+e^{-bt}}## leads to a mess of exponential functions, and does not bring me closer to a solution. Perhaps there is some other way, using tricks specific to calculating Fourier transforms that could be helpful here?
Any suggestions are most appreciated
J
I am trying to determine the Fourier transform of the hyperbolic tangent function. I don't have a lot of experience with Fourier transforms and after searching for a bit I've come up empty handed on this specific issue.
So what I want to calculate is:
##\int\limits_{-\infty}^\infty e^{-it\omega}\text{tanh}(bt) dt##
where ##b## is some constant.
Using ##\text{tanh}(bt)=\frac{e^{bt}-e^{-bt}}{e^{bt}+e^{-bt}}## leads to a mess of exponential functions, and does not bring me closer to a solution. Perhaps there is some other way, using tricks specific to calculating Fourier transforms that could be helpful here?
Any suggestions are most appreciated
J