Cross correlation for two m-sequences

In summary: The final result is the cross correlation function for the two m-sequences, with the maximum value indicating the shift position where the sequences match the most. In this case, the maximum value is 4 at shift position 1.In summary, to calculate the discrete period cross correlation function for a pair of m-sequences, you can write out the sequences in polynomial form, expand them, create a table, and calculate the cross correlation function for each shift position. The maximum value of the cross correlation function indicates the shift position with the best match between the
  • #1
Fiona Rozario
55
1
Calculate the discrete period cross correlation function for the pair of m-sequences given by -
G1(D) = 1 + D2 + D5 and G2(D) = 1 + D2 + D3 - D4+ D5


I started by drawing the shift register diagrams and calculating each state, but that is a long process and I don't know how would i show the cross correlation in an equation form. Help please...
 
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  • #2


To calculate the discrete period cross correlation function for these two m-sequences, you can use the following steps:

1. Write out the two m-sequences in polynomial form:
G1(D) = 1 + D^2 + D^5
G2(D) = 1 + D^2 + D^3 - D^4 + D^5

2. Expand the polynomials to get the full sequences:
G1(D) = 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, ...
G2(D) = 1, 0, 1, 1, -1, 1, 0, 0, 0, 0, 0, ...

3. Calculate the length of the sequences, which is the period of the m-sequences. In this case, the period is 11.

4. Create a table with the two sequences, with the first sequence shifted by one position for each row:
G1(D) = 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, ...
G2(D) = 0, 1, 0, 1, 1, -1, 1, 0, 0, 0, 0, ...

5. Multiply the two sequences element-wise and sum the products for each row. This will give you the cross correlation function for each shift position:
Cross correlation function for shift position 0: 1*0 + 0*1 + 1*0 + 0*1 + 0*1 + 1*(-1) + 0*1 + 0*0 + 0*0 + 0*0 + 0*0 = -1
Cross correlation function for shift position 1: 1*1 + 0*0 + 1*1 + 0*1 + 0*1 + 1*1 + 0*(-1) + 0*0 + 0*0 + 0*0 + 0*0 = 4
Cross correlation function for shift position 2: 1*0 + 0*1 + 1*1 + 0*(-1) + 0*1 + 1*0 +
 

1. What is cross correlation for two m-sequences?

Cross correlation for two m-sequences is a mathematical technique used to measure the similarity between two pseudorandom binary sequences, also known as m-sequences. It involves multiplying one sequence by the reversed version of the other sequence and then summing up the products. The resulting value indicates the level of similarity between the two sequences.

2. How is cross correlation calculated for two m-sequences?

To calculate cross correlation for two m-sequences, first the two sequences are multiplied together, element by element. Then, the resulting sequence is reversed and the products are summed up. The resulting sum is the cross correlation value.

3. What is the significance of cross correlation for two m-sequences?

Cross correlation for two m-sequences is used to determine the level of correlation between two sequences. This is important in signal processing and communication systems, as it helps to detect and correct errors in data transmission.

4. Can cross correlation be negative?

Yes, cross correlation can be negative. This indicates that the two sequences are negatively correlated, meaning that they are dissimilar to each other.

5. Are there any limitations to using cross correlation for two m-sequences?

One limitation of using cross correlation for two m-sequences is that it assumes the sequences are of equal length and have the same starting point. If this is not the case, the resulting correlation value may not accurately reflect the true level of correlation between the sequences.

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