# Question: Consider the periodic sequence generated by the four stage shift

Consider the periodic sequence generated by the four- stage shift register in Figure 12.1. Suppose the sequence is converted to ±1- valued sequence by mapping all 1’s to – 1’s and all 0’s to 1’s. One period of the resulting sequence is:

– 1,– 1,– 1,– 1,1,1,1,– 1,1,1,– 1, –1,–1,1

Calculate the autocorrelation function of this periodic sequence. Note: Do not just treat this sequence as having finite length. The sequence is infinite in both directions. The finite sequence shown above is just one period of the infinite periodic sequence.

– 1,– 1,– 1,– 1,1,1,1,– 1,1,1,– 1, –1,–1,1

Calculate the autocorrelation function of this periodic sequence. Note: Do not just treat this sequence as having finite length. The sequence is infinite in both directions. The finite sequence shown above is just one period of the infinite periodic sequence.

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