EE4253 Digital Communications
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada
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).
Circuit based on P(x) = x3+x2+1
|Sequence #1 (Starting with 0)|
|States: 0 ⇒ 0, forever...|
|Sequence #2 (Starting with 1)|
|States: 1 ⇒ 4 ⇒ 6 ⇒ 7 ⇒ 3 ⇒ 5 ⇒ 2 ⇒ 1|
|Period = 7 (Maximum Length Sequence)
Output = 1001110...
|A maximum length sequence was found. For this polynomial of degree 3, the maximum length sequence has a period of 23-1 states. This only happens when the characteristic polynomial is prime, as in this case. Use of a prime polynomial is a necessary but not sufficient condition for a maximum length sequence. For example, try 1001001 which is prime, but does not give a maximum length sequence.|
|Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates.|
Wed May 22 04:26:26 ADT 2013
Last Updated: 28 NOV 98
|Richard Tervo [ firstname.lastname@example.org ]||Back to the course homepage...|