For a homework assignment, I was asked "What happens when you take the discrete IFT of a continuous FT," where the given forward transform is:
$G(k)$ = $\int_{-\infty}^\infty g(x)e^{-2 \pi xk}dx$
and the discrete transform is
$d_j = \sum_{j'=0}^{(N-1)}G_{j'}e^{2 \pi i \frac{(j'j)}{N}}$
From what I understand, this problem is related to the overarching concepts in MRI of converting continuous signals into some continuous "k-space" representation, then converting it back to some discrete representation of the original signal. I am having a very hard time coming up with something to show this "rigorously," and I'm lacking some confidence in my understanding in this problem.
Could anyone help me get started? Best-