Main Content

Filter data using polynomials over prime Galois field

`y = gffilter(b,a,x)`

y = gffilter(b,a,x,p)

**Note**

This function performs computations in GF(p^{m}), where p is prime.
To work in GF(2^{m}), use the `filter`

function with
Galois arrays. For details, see Filtering.

`y = gffilter(b,a,x)`

filters the data in vector
`x`

with the filter described by vectors `b`

and
`a`

. The vectors `b`

, `a`

and
`x`

must be in GF(2), that is, be binary and `y`

is also in
GF(2).

`y = gffilter(b,a,x,p)`

filters the data
`x`

using the filter described by vectors `a`

and
`b`

. `y`

is the filtered data in GF(`p`

).
`p`

is a prime number, and all entries of `a`

and
`b`

are between 0 and `p`

-1.

By definition of the filter, `y`

solves the difference equation

a(1)y(n) = b(1)x(n)+b(2)x(n-1)+b(3)x(n-2)+...+b(B+1)x(n-B) -a(2)y(n-1)-a(3)y(n-2)-...-a(A+1)y(n-A)

where

`A`

+1 is the length of the vector`a`

`B`

+1 is the length of the vector`b`

`n`

varies between 1 and the length of the vector`x`

.

The vector `a`

represents the degree-n_{a} polynomial

a(1)+a(2)x+a(3)x^`2`

+...+a(A+1)x`^A`

The impulse response of a particular filter is given in the code and diagram below.

b = [1 0 0 1 0 1 0 1]; a = [1 0 1 1]; y = gffilter(b,a,[1,zeros(1,19)]); stem(y); axis([0 20 -.1 1.1])