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 |
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])