I have two sequences,
- Let $A$ be the first sequence whose dimensions are $(5, 5, 3)$ takes complex values
- Let $B$ be the second sequence whose dimensions are $(5, 5, 1)$ also takes complex values
I would like to use $\mathrm{fftw}$ to perform fast convolution to get the output $C$. I presume the output dimension is also $(5,5,3)$? But I am confused.
My questions are,
- Is output dimension correct? For $\mathrm{1d}$ the output length is $M+N -1$, presume the $M$ and $N$ are the lengths of some sequence $R$ and $S$. But I can't figure out for $\mathrm{3d}$ data.
- How to zero-pad $B$, in-case zero padding is necessary? Is it like increasing the $z$ dimension to $3$ to make it $(5, 5, 3)$ for $B$ too?