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## Homework Statement

For a periodic sawtooth function ##f_p (t) = t## of period ##T## defined over the interval ##[0, T]##, calculate the Fourier transform of a function made up of only a single period of ##f_p (t),## i.e.

$$f(t)=\left\{\begin{matrix}f_p (t) \ \ 0<t<T\\0 \ \ elsewhere \end{matrix}\right.$$

Use the result that

$$FT \Big[ f(t) = t \Big] = \frac{j \delta' (\nu)}{2 \pi}$$

## Homework Equations

## The Attempt at a Solution

I am not sure how to approach this problem. I think somehow we need to evaluate ##f(\nu) = \frac{j \delta' (\nu)}{2 \pi}## over the interval ##[0, T]##, but it's not possible since we are in Fourier space. If this is the case, do we need to write the interval in terms of the corresponding frequency (##[\nu = 0, \ 1/T ]##)?

Any help would be greatly appreciated.