
	ECE4253 Digital Communications

	Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Linear Recursive Sequence Generator

Shift registers with feedback essentially divide polynomials to create distinctive binary sequences.

This online tool draws and analyzes digital circuits which generate Linear Recursive Sequences (LRS) based on a defining polynomial P(x). The circuit shown below is traced through all possible states. Maximum length sequences are identified. The autocorrelation of each sequence can also be checked (maximum 1023 bits).

Fibonacci Implementation

alternate configuration Fibonacci

Circuit based on P(x) = x⁵+x³+1

The circuit taps correspond to P(x) = (101001).

Taps: (101001) (prime)

Sequence #1 (Starting with 0)

States: 0 0 forever...

Sequence #2 (Starting with 1)

States: 1 16 8 20 10 21 26 29 14 23 27 13 6 3 17 24 28 30 31 15 7 19 25 12 22 11 5 18 9 4 2 1

Period = 31 (Maximum Length Sequence) (autocorrelation)
Output = 1000010101110110001111100110100...

See a detailed analysis and State Table for this circuit.

Specify the taps for your sequence

Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates.


2024-12-06 07:19:27 AST Last Updated: 2014-01-13	Richard Tervo [ tervo@unb.ca ]	Back to the course homepage...