- #1

cepheid

Staff Emeritus

Science Advisor

Gold Member

- 5,192

- 38

[tex] x(t) = \theta(t-t_1) - \theta(t-t_2) [/tex]

Assume [itex] t_2 > t_1 [/itex]

and we are asked to find the fourier transform. So I wrote down:

[tex] x(\omega) = \int_{-\infty}^{\infty}{e^{-i\omega t} [\theta(t-t_1) - \theta(t-t_2)] dt} [/tex]

I know that the function given is the heaviside step function. Its derivative is the dirac delta function, and it is itself the derivative of the ramp function. But I just found this stuff out by looking online. We've learned neither convolution nor fourier transform in math class, yet somehow this physics prof expects us to do it. Can someone at least point me in the right direction?

Thanks.