Question

Please answer the following

What is the relationship between polynomials for shift registers and polynomials for analog filters?

Answer 1

Polynomials for shift registers:

The bit positions that affect the next state of shift register are called the taps.

The arrangement of taps for feedback in an SR can be expressed as a polynomial mod 2. This means that the coefficients of the polynomial must be 1s or 0s. This is called the feedback polynomial or reciprocal characteristic polynomial.

For example, if the taps are at the 16th, 14th, 13th and 11th bits (as shown), the feedback polynomial is

x^{16}+x^{14}+x^{13}+x^{11}+1.

Polynomials for analog filters:

These are not represented as 1s and 0s as in shift registers.

As we know these are the combinations of coefficients and state values:

Ex. b0. x(n) + b1.x(n-1) + ..... bn.x(N)