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filter (gf)

1-D digital filter over Galois field


y = filter(b,a,x)
[y,zf] = filter(b,a,x)


y = filter(b,a,x) filters the data in the vector x with the filter described by numerator coefficient vector b and denominator coefficient vector a. The vectors b, a, and x must be Galois vectors in the same field. If a(1) is not equal to 1, filter normalizes the filter coefficients by a(1). As a result, a(1) must be nonzero.

The filter is a "Direct Form II Transposed" implementation of the standard difference equation below.

a(1)*y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb) ...
                      - a(2)*y(n-1) - ... - a(na+1)*y(n-na)

[y,zf] = filter(b,a,x) returns the final conditions of the filter delays in the Galois vector zf. The length of the vector zf is max(size(a),size(b))-1.


An example is in Huffman Coding.

Introduced before R2006a

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