ECE4253 Digital Communications Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

# Binary Sequence Correlation Tool

This online tool computes the correlation of periodic binary sequence. In particular, maximum length Linear Recursive Sequences (LRS) have distinct autocorrelation properties.

# Binary Sequence

For correlation, ones and zeros are replaced by +1 and -1 respectively

 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 ... ... + - - - - - + + + - - - - + - - + - - - + + - + + - - + - + + - ...

# Correlation Result

The correlation of a sequence with itself is autocorrelation. The autocorrelation result has a period of 63 bits corresponding to the length of the supplied sequence. The graph shows two full periods of the autocorrelation result. The first 32 values in the correlation output are shown below.
```
63 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...

```

# Input Sequences

Enter two binary sequences (A,B) to be correlated. For autocorrelation, only the first sequence (A) is required.

Binary Sequence A:
Binary Sequence B:
Example Maximum Length Sequences: [ 7-bit ] [ 15-bit ] [ 31-bit ] [ 63-bit ]

# Special Sequences - Barker Code

Each Barker code below may also be inverted and bit-reversed. [bits]

 [2] + + [2] + - [3] + - - [4] + - - - [4] - + - - [5] + + + - + [7] + + + - - + - [11] + + + - - - + - - + - [13] + + + + + - - + + - + - +

Ref: R. H. Barker, Group synchronization of binary digital systems, in Communication Theory, W. Jackson, Ed. London, U.K.: Butterworths, 1953, pp. 273-287.

 2024-08-14 11:39:55 ADT Last Updated: 04-09-05 Richard Tervo [ tervo@unb.ca ]