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FIR FILTER DECOMPOSITION & TRANSFER FUNCTION

Asked by Yvan on 15 Feb 2013

Hi,

I have a FIR filter (with 0 at DC) that I would like to decompose in N FIR fiters.

My original filter is a (3*3) filter that I use on medical images (3-bit) : H = [2 1 2; 2 0 2; 2 1 2]/14;

And I want to decompose it into 7 "FIR" filters (to treat finite states), such as:

H1 = [0 0 0; 1 0 1; 0 0 0];

H2 = [0 1 0; 1 0 1; 0 1 0];

H3 = [0 1 1; 1 0 1; 1 1 0];

H4 = [1 1 1; 1 0 1; 1 1 1];

H5 = [1 1 1; 2 0 2; 1 1 1];

H6 = [1 1 2; 2 0 2; 2 1 1];

H7 = [2 1 2; 2 0 2; 2 1 2];

I use freqz2 to represent the transfer function of my original filter. But in the case of finite FIR filters, I don´t know how to represent the overall transfer function of those 7 filters. Does this system can be compared with a polyphase FIR filters? How can I represent the overall transfer function of my image process?

Thanks for the help

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