I have a function $\mu(x)$ that I need to convolve with several functions $\nu_n(x)$. I'm currently taking the DFT of $\mu$ and multiplying it individually with the N DFTs of the functions $\nu_n$ and then taking the inverse DFT to obtain the convolution.
Can I instead define $m(x, y) = \mu(x), n(x, y) = \nu_y(x)$ for discrete $y$, take the 2D DFT to obtain $M(u, v)$ and $N(u, v)$, which I then multiply element wise as $C(u, v) = M(u, v) N(u, v)$ and then take the inverse 2D DFT to obtain the same result $c(x, y)$ as I did elementwise in the above method?
