# Constraints for Type 3 Linear Phase Filter

This might be a strange question - but most of the Type 3 LPF I'm seeing are having this in common for $$h[n]$$, assuming $$h[n]$$ is real:

1. We cannot have outermost element of h[n] lower than middle elements
2. (or) Have middle element lower than outermost elements.

Eg: if filter coefficients are $$[3,2,1,0,-1,-2,-3]$$, it there any restriction for a type $$3$$ filter to not have $$[1,2,3,0,-3,-2,-1]$$ as a possible LPF $$h[n]$$?

(Please excuse my ignorance if this is a basic question - I'm quite new FIR Filter design). And I've gone through quite a few design docs before asking this question - none of them mention this, so I'm guessing this is not a req? Yet the diagrams seem to indicate this, hence the question...

There is no such restriction for a type III linear phase filter. Neither is there such a restriction for any other type of linear phase filter. Type III linear phase filters have an odd filter length $$N$$ and odd symmetry. I.e., as long as the filter's impulse response $$h[n]$$ satisfies
$$h\left[\frac{N-1}{2}+n\right]=-h\left[\frac{N-1}{2}-n\right]$$