a$)$ Can you think of a way to use the Fourier transform to compute $($or partially compute$)$ the magnitude of the gradient

$[$Eq$.(3-58)]$ for use in image differentiation? If your answer is yes, give a method to do it$.$ If your answer is no$,$ explain why?

$M(x,y)=||gradf||=$mag$(gradf)=\sqrt[\phantom{2}]{g_x^2+g_y^2}$

b$)$ Show that tilde$(F)()$ in Eq$.(4-40)$ is infinitely periodic in both directions, with period $\frac{1}{}T.$

tilde$(F)()={\displaystyle \underset{-}{\overset{}{}}}$tilde$(f)(t)e^{-j2t}dt={\displaystyle \underset{-}{\overset{}{}}}{\displaystyle \underset{n=-}{\overset{}{}}}f(t)(t-nT)e^{-j2t}dt$

$={\displaystyle \underset{n=-}{\overset{}{}}}{\displaystyle \underset{-}{\overset{}{}}}f(t)(t-nT)e^{-j2t}dt$

$={\displaystyle \underset{n=-}{\overset{}{}}}{f}_n{e}^{-j2nT}$