gffilter (Communications Toolbox)

Filter data using polynomials over a prime Galois field

Syntax

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

Description

Note This function performs computations in GF(p^m) where p is odd. To work in GF(2^m), use the filter function with Galois arrays. For details, see Filtering.

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
```

Examples

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])

See Also
gfconv, gfadd, filter

gfdiv gflineq