| Communications Toolbox | |
Filter data using polynomials over a prime Galois field
y = gffilter(b,a,x,p)
Note This function performs computations in GF(pm) where p is odd. To work in GF(2m), 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-na 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])
gfconv, gfadd, filter, Galois Fields of Odd Characteristic
| | gfdiv | gflineq | |
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