This may sound weird but can FIR filters be realized by implementing it in parallel form like in IIR? I know that FIR can be realized in cascade, but I can't seem to find any resources that realize FIR using parallel.
Is it possible? And if not, why not?
The typical references to "parallel FIR" filters (such as this link: https://download.atlantis-press.com/article/23421.pdf) are polyphase implementations to reduce the resource (processing rate) requirements on any one filter by being able to run each filter at a fraction of the rate required to realize the same processing result as a single FIR filter. In that sense we are parallelizing the filter to share resources in contrast to representing IIR filters in additive forms of lower order (arrived at using partial fraction expansion).
Note that when you cascade two filters you convolve the coefficients which is polynomial multiplication (so the product of the filter polynomials). When you alternatively implement filters in parallel form you are performing an addition of the coefficients raised to the same power of z. So for example the parallel form of the following two FIR filters given as:
$$H_1(z)= a + b z^{-1} + c z^{-2}$$ $$H_2(z) = d + e z^{-1} + f z^{-2}$$
An actual parallel implementation would result in the trivial addition of the two in $z$ as:
$$H_1(z) +H_2(z) = (a+d) + (b+e) z^{-1} + (c+f) z^{-2}$$
Unlike IIR forms where the same process of addition exists, the utility of this would be to recognize how such structures can be easily combined when simplifying more complicated block diagrams rather than reduce a given FIR filter into a parallel structure each with lower order. Although similar to this where there is indeed a notable advantage is the implementation of polyphase structures which have a parallel form (but include a commutation function between the parallel filters). Most references to actual "parallel FIR" implementations where parallelization is done for latency reduction and optimizing resources is a polyphase filter implementation. I describe the parallelization and implementation details of polyphase filters further at this post: How to implement Polyphase filter?
Other commonly used filter structures for both FIR and IIR filters are referred to as "Direct Form 1", "Direct Form II", transposed, cascade, frequency sampling, lattice and lattice-ladder as well as the polyphase structures already mentioned.
If by "parallel form" you mean "parallel sections" as compared to "cascaded sections", the answer is "not really".
An FIR is can be considered an IIR with all the poles at $z=0$. You can technically go through the motions of doing partial fractional expansion with multiple roots but you are just going to end up with the exact same FIR filter again and all the lower order sections will be zero.
