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gffilter (prime Galois field)

Filter data using polynomials over prime Galois field


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



This function performs computations in GF(pm), where p is prime. To work in GF(2m), 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+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-na polynomial



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)]);
axis([0 20 -.1 1.1])

Version History

Introduced before R2006a

See Also