# Homework Help: 2D FIR Filter & Finite Decomposition

1. Feb 18, 2013

### rivulatus

Hi All,

I would like to know how can I call or express the following process!

I use a (3x3) 2D FIR Filter for imaging processing with DC = 0, like this:

0 1 1
2 O 2 /8
1 1 0

My filter is such that I can decompose it into finite sates, as my image (medical)
can take 9 finite state (from 0 to 8 ). So instead of having 1 linear FIR filter for
all the states, I have a "FIR" filter for each state. I decompose my filter like that,
where H? is the state

H1 = 0 0 0
0 0 1
0 0 0

H2 = 0 0 0
1 0 1
0 0 0

H3 = 0 0 0
1 0 1
0 1 0

H4 = 0 1 0
1 0 1
0 1 0

H5 = 0 1 1
1 0 1
0 1 0

H6 = 0 1 1
1 0 1
1 1 0

H7 = 0 1 1
2 0 1
1 1 0

H8 = 0 1 1
2 0 2
1 1 0

Obviously, there is no filter for H0, and I notice that it result in a smoother filtration.

I would like to know if there is a term to describe this process?
How can I call it? (is it related to polyphase FIR?)

Where can I find documentation regarding such a process?

Thanks a lot for your help