1
$\begingroup$

I am learning about image processing. Currently, I am reading about upsampling and down sampling. Here is some background what I am reading:

enter image description here

enter image description here

I was wondering if someone show me a proof of how equation (70) is true. It simply says "It can be shown that".

Thanks!

$\endgroup$
3
$\begingroup$

HINT:

First of all, Eq. $(70)$ is wrong, there's an imaginary unit $j$ missing in the exponent. If you add that missing $j$, note that for $n=kM$, $k\in\mathbb Z$, you have $e^{j2\pi ln/M}=1$, so the result of the scaled sum equals $1$. In order to see that the sum equals zero for all other values of $n$, use the formula of the geometric series.

This answer is also relevant to your question.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.