Prove that [begin{equation*}mathcal{F}^{-1}left{sum_{k=-infty}^{infty} deltaleft(omega-frac{2 pi}{N} k ight) ight}=frac{N}{2 pi} sum_{p=-infty}^{infty} delta(n-N p) tag{2.262} end{equation*}] by computing its

Prove that

\[\begin{equation*}\mathcal{F}^{-1}\left\{\sum_{k=-\infty}^{\infty} \delta\left(\omega-\frac{2 \pi}{N} k\right)\right\}=\frac{N}{2 \pi} \sum_{p=-\infty}^{\infty} \delta(n-N p) \tag{2.262} \end{equation*}\]

by computing its left-hand side with the inverse Fourier transform in Equation (2.207) and verify that the resulting sequence is equal to its right-hand side.