![]() It doesn't matter if this number is positive or negative. Likewise, multiplying with an odd number is equivalent to multiplying with 1. In fact, multiplying with an even number is equivalent to multiplying with 0. All multiplications involve only integers.The plus operator in this field is equivalent to a XOR.However, it's also possible to apply this theory on GF(2), which is the finite field (Galois Field) that consists of two numbers: 0 and 1. FIRs and IIRs) is usually applied on the field of complex numbers. The rest of this page shows why this is not a coincidence.įor a general explanation about LFSRs, refer to the Wikipedia page on this topic. The degree of the polynomial is n=16, so each x i in G(x) is represented in F(x) by x n-i. The Fibonacci polynomial (or feedback polynomial) is this: The implementations of the LFSRs are completely different. The same LFSR can be implemented in Fibonacci form, as shown in this drawing:ĭespite the similarity between these two drawings, the directions of the arrows are reversed. Note that the exponents in the polynomial (3, 4, and 5) reflect the number of delay elements on the left side of each XOR. ![]() ![]() ![]() The representation of this LFSR as a Galois polynomial is: This page can be summarized in one sentence: If you want to convert an LFSR's polynomial from Galois form to Fibonacci form, reverse the order of the coefficients.įor example, this is the drawing for the LFSR that is often used in scramblers:Įach block that is marked with D is a delay of one clock cycle. ![]()
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